#include <bits/stdc++.h>
#define pb push_back
#define f first
#define sc second
using namespace std;
typedef long long int ll;
typedef string str;
struct sparse_table{
vector<int> lg;
vector<vector<pair<int, int>>> v;
sparse_table(vector<int> _v){
int n = _v.size();
lg.resize(n+1);
for(int i = 0; i <= n; i++) lg[i] = log2(i);
int k = 0, p = 1;
while(p < n) p*=2, k++;
k++;
v = vector<vector<pair<int, int>>>(n, vector<pair<int, int>>(k, make_pair(0, 0)));
for(int i = 0; i < n; i++) v[i][0] = {_v[i], i};
for(int p = 1; p < k; p++){
for(int i = 0; i < n; i++){
v[i][p] = max(v[i][p], v[i][p-1]);
if(i + (1<<(p-1)) < n) v[i][p] = max(v[i][p], v[i + (1<<(p-1))][p-1]);
}
}
}
pair<int, int> query(int a, int b){
int p = lg[b-a+1];
return max(v[a][p], v[b-(1<<p)+1][p]);
}
};
const int K = 21;
const int inf = 1e9;
int n;
vector<int> h;
vector<int> jump[2];
vector<int> anc[2][K];
sparse_table sp({});
template<int k>
int get_anc(int nd, int h){
for(int i = 0; i < K; i++){
if(h%2 == 1) nd = anc[k][i][nd];
h/=2;
}
return nd;
}
template<int k>
int binlift(int nd, int l){
if(h[nd] >= l) return 0;
for(int i = K-1; i >= 0; i--) if(h[anc[k][i][nd]] <= l)
return binlift<k>(anc[k][i][nd], l)+(1<<i);
return 0;
}
void init(int N, vector<int> H){
for(int &x: H) x--;
n = N, h = H;
h.pb(n);
fill(jump, jump+2, vector<int>(n, n));
fill(anc[0], anc[0]+K, vector<int>(n+1, n));
fill(anc[1], anc[1]+K, vector<int>(n+1, n));
sp = sparse_table(H);
stack<int> st;
for(int i = n-1; i >= 0; i--){
while(!st.empty() && h[i] > h[st.top()]){
jump[0][st.top()] = i;
st.pop();
}
st.push(i);
}
while(!st.empty()) st.pop();
for(int i = 0; i < n; i++){
while(!st.empty() && h[i] > h[st.top()]){
jump[1][st.top()] = i;
st.pop();
}
st.push(i);
}
while(!st.empty()) st.pop();
for(int i = 0; i < n; i++){
anc[0][0][i] = h[jump[0][i]] < h[jump[1][i]] ? jump[0][i] : jump[1][i];
anc[1][0][i] = h[jump[0][i]] > h[jump[1][i]] ? jump[0][i] : jump[1][i];
if(anc[1][0][i] == n) anc[1][0][i] = anc[0][0][i];
}
for(int p = 1; p < K; p++) for(int i = 0; i <= n; i++)
anc[0][p][i] = anc[0][p-1][anc[0][p-1][i]],
anc[1][p][i] = anc[1][p-1][anc[1][p-1][i]];
}
int minimum_jumps(int A, int B, int C, int D){
int l = 1, r = B-A+1;
int m1 = 0, m2 = sp.query(C, D).f;
if(B+1 < C) m1 = sp.query(B+1, C-1).f;
if(m1 > m2) return -1;
while(l < r){
int md = (l+r)/2;
if(sp.query(B-md+1, B).f > m2) r = md;
else l = md+1;
}
int S = A;
if(sp.query(B-l+1, B).f > m2){
S = B-l+2;
if(S > B) return -1;
}
S = sp.query(S, B).sc;
int ans = binlift<1>(S, m1);
int nd = get_anc<1>(S, ans);
if(h[nd] >= m1 && h[nd] <= m2) return ans+1;
if(h[anc[1][0][nd]] <= m2) return ans+2;
int x = binlift<0>(nd, m1);
nd = get_anc<0>(nd, x);
ans+=x;
if(h[nd] >= m1 && h[nd] <= m2) return ans+1;
if(h[anc[1][0][nd]] <= m2) return ans+2;
return -1;
}
