// Om Namah Shivaya
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x, y) ((x + y - 1) / (y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i, n) for(int i = 0; i < n; ++i)
#define rep1(i, n) for(int i = 1; i <= n; ++i)
#define rev(i, s, e) for(int i = s; i >= e; --i)
#define trav(i, a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a, b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a, b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
read the edi a long time ago: have faint memories from it
*/
const int MOD = 1e9 + 7;
const int N = 2e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "jumps.h"
template<typename T>
struct sparse_table {
/*============================*/
T merge(T a, T b) {
return max(a,b);
}
/*============================*/
vector<vector<T>> table;
vector<int> bin_log;
int LOG = 0;
sparse_table() {
}
sparse_table(vector<T> &a, int n) {
while ((1 << LOG) <= n) LOG++;
table = vector<vector<T>>(n, vector<T>(LOG));
bin_log = vector<int>(n + 1);
rep(i, n) table[i][0] = a[i];
rep1(j, LOG - 1) {
rep(i, n) {
int jump = 1 << (j - 1);
if (i + jump >= n) {
break;
}
table[i][j] = merge(table[i][j - 1], table[i + jump][j - 1]);
}
}
bin_log[1] = 0;
for (int i = 2; i <= n; ++i) {
bin_log[i] = bin_log[i / 2] + 1;
}
}
T query(int l, int r) {
int len = r - l + 1;
int k = bin_log[len];
T val1 = table[l][k];
T val2 = table[r - (1 << k) + 1][k];
return merge(val1, val2);
}
};
const int LOG = 18;
int upl[N][LOG], upr[N][LOG], upb[N][LOG];
vector<int> a;
sparse_table<int> sparse;
vector<int> pos_of_val;
void init(int n, vector<int> h) {
a = h;
a.pb(inf1);
sparse = sparse_table<int>(a,n+1);
pos_of_val = vector<int>(n+5);
rep(i,n) pos_of_val[a[i]] = i;
vector<int> ngel(n,n), nger(n,n);
stack<int> st;
rep(i,n){
while(!st.empty() and a[i] > a[st.top()]){
nger[st.top()] = i;
st.pop();
}
st.push(i);
}
while(!st.empty()) st.pop();
rev(i,n-1,0){
while(!st.empty() and a[i] > a[st.top()]){
ngel[st.top()] = i;
st.pop();
}
st.push(i);
}
while(!st.empty()) st.pop();
rep(j,LOG){
upl[n][j] = upr[n][j] = upb[n][j] = n;
}
rep(i,n){
upl[i][0] = ngel[i];
upr[i][0] = nger[i];
if(a[ngel[i]] > a[nger[i]]){
upb[i][0] = ngel[i];
}
else{
upb[i][0] = nger[i];
}
}
rep1(j,LOG-1){
rep(i,n){
upl[i][j] = upl[upl[i][j-1]][j-1];
upr[i][j] = upr[upr[i][j-1]][j-1];
upb[i][j] = upb[upb[i][j-1]][j-1];
}
}
}
int minimum_jumps(int l1, int l2, int r1, int r2) {
if(r1 != r2){
int ans = inf1;
for(int r = r1; r <= r2; ++r){
int res = minimum_jumps(l1,l2,r,r);
if(res != -1){
amin(ans,res);
}
}
if(ans == inf1) ans = -1;
return ans;
}
int l = -1, r = r1;
if(l1 <= r and r <= l2){
return 0;
}
if(l2 < r){
// some suff is good
int lo = l1, hi = l2;
int suff = -1;
while(lo <= hi){
int mid = (lo+hi) >> 1;
if(sparse.query(mid,r) <= a[r]){
suff = mid;
hi = mid-1;
}
else{
lo = mid+1;
}
}
if(suff == -1) return -1;
int mx = sparse.query(suff,l2);
l = pos_of_val[mx];
}
else{
// some pref is good
int lo = l1, hi = l2;
int pref = -1;
while(lo <= hi){
int mid = (lo+hi) >> 1;
if(sparse.query(r,mid) <= a[r]){
pref = mid;
lo = mid+1;
}
else{
hi = mid-1;
}
}
if(pref == -1) return -1;
int mx = sparse.query(l1,pref);
l = pos_of_val[mx];
}
int ans = 0;
// big jumps until possible
rev(j,LOG-1,0){
int nxt = upb[l][j];
if(a[nxt] <= a[r]){
l = nxt;
ans += (1 << j);
}
}
// small jumps going in one direction until reach r
rev(j,LOG-1,0){
int nxt = upl[l][j];
if(a[nxt] <= a[r]){
l = nxt;
ans += (1 << j);
}
}
rev(j,LOG-1,0){
int nxt = upr[l][j];
if(a[nxt] <= a[r]){
l = nxt;
ans += (1 << j);
}
}
return ans;
/*
{
int ans = 0;
while(l != r){
int lx = upl[l][0], rx = upr[l][0];
if(a[lx] > a[r]){
l = rx;
}
else if(a[rx] > a[r]){
l = lx;
}
else{
if(a[lx] > a[rx]){
l = lx;
}
else{
l = rx;
}
}
ans++;
}
return ans;
}
*/
}
