#include <bits/stdc++.h>
#include "jumps.h"
using namespace std;
using ll = long long;
using ld = long double;
#define fi first
#define se second
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int, int>
#define pll pair<long long, long long>
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng64(chrono::steady_clock::now().time_since_epoch().count());
inline int rand(int l,int r){return uniform_int_distribution<int>(l, r)(rng);}
inline ll rand(ll l,ll r){return uniform_int_distribution<ll>(l, r)(rng64);}
#ifdef DEBUG
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
const int MAXN = 5e5 + 7;
const int MAXK = 22;
int lg[MAXN];
int mx[MAXK][MAXN];
int jumpL[MAXK][MAXN];
int jumpP[MAXK][MAXN];
int tab[MAXN];
int n;
bool distCount = 0;
int getMx(int l, int p){
if(p < l){
return 0;
}
return max(mx[lg[p - l + 1]][l], mx[lg[p - l + 1]][p - (1 << lg[p - l + 1]) + 1]);
}
int getMxP(int ind){
if(getMx(ind + 1, n - 1) <= tab[ind]){
return -1;
}
int l = ind + 1;
int p = n - 1;
int s;
while(l < p){
s = (l + p) / 2;
if(getMx(ind + 1, s) <= tab[ind]){
l = s + 1;
}else{
p = s;
}
}
return l;
}
int getMxL(int ind){
if(getMx(0, ind - 1) <= tab[ind]){
return -1;
}
int l = 0;
int p = ind - 1;
int s;
while(l < p){
s = (l + p + 1) / 2;
if(getMx(s, ind - 1) <= tab[ind]){
p = s - 1;
}else{
l = s;
}
}
return l;
}
void init(int N, vi H) {
n = N;
bool f = 1;
for(int i = 0; i < n; i++){
tab[i] = H[i];
if(tab[i] != i + 1){
f = 0;
}
}
if(f){
distCount = 1;
return;
}
for(int i = 2; i < MAXN; i++){
lg[i] = lg[i / 2] + 1;
}
for(int i = 0; i < n; i++){
mx[0][i] = tab[i];
}
for(int j = 1; j < MAXK; j++){
for(int i = 0; i < n; i++){
mx[j][i] = max(mx[j - 1][i], mx[j - 1][min(n - 1, i + (1 << (j - 1)))]);
}
}
for(int i = 0; i < n; i++){
jumpL[0][i] = getMxL(i);
jumpP[0][i] = getMxP(i);
}
for(int j = 1; j < MAXK; j++){
for(int i = 0; i < n; i++){
if(jumpL[j - 1][i] != -1){
jumpL[j][i] = jumpL[j - 1][jumpL[j - 1][i]];
}
if(jumpP[j - 1][i] != -1){
jumpP[j][i] = jumpP[j - 1][jumpP[j - 1][i]];
}
}
}
}
int dist(int a, int b){
int ans = 1e9;
int akt = a;
int res = 0;
for(int j = MAXK - 1; j >= 0; j--){
if(jumpP[j][akt] != -1 && jumpP[j][akt] < b){
akt = jumpP[j][akt];
res += (1 << j);
}
}
res++;
akt = jumpP[0][akt];
if(akt == b){
ans = res;
}
if(getMx(0, a - 1) > tab[a]){
res = 0;
akt = a;
int l = 0;
int p = a - 1;
int s;
while(l < p){
s = (l + p) / 2;
if(getMx(s, a - 1) <= tab[a]){
p = s - 1;
}else if(getMx(s, a - 1) >= tab[b]){
l = s + 1;
}else{
p = s;
}
}
if(tab[l] > tab[a] && tab[l] < tab[b]){
for(int j = MAXK - 1; j >= 0; j--){
if(jumpL[j][akt] != -1 && jumpL[j][akt] > l){
akt = jumpL[j][akt];
res += (1 << j);
}
}
res++;
akt = jumpL[0][akt];
if(akt == l){
for(int j = MAXK - 1; j >= 0; j--){
if(jumpP[j][akt] != -1 && jumpP[j][akt] < b){
akt = jumpP[j][akt];
res += (1 << j);
}
}
res++;
akt = jumpP[0][akt];
if(akt == b){
ans = min(ans, res);
}
}
}
}
if(ans == 1e9){
return -1;
}
return ans;
}
int minimum_jumps(int A, int B, int C, int D){
if(distCount){
return C - B;
}
if(getMx(B + 1, C - 1) >= getMx(C, D)){
return -1;
}
if(A == B && C == D){
return dist(A, C);
}
vi dist(n, 1e9);
queue<int> q;
vi vis(n, 0);
for(int i = A; i <= B; i++){
vis[i] = 1;
q.push(i);
dist[i] = 0;
}
while(sz(q)){
int v = q.front();
q.pop();
int akt = getMxL(v);
if(akt != -1 && !vis[akt]){
q.push(akt);
vis[akt] = 1;
dist[akt] = dist[v] + 1;
}
akt = getMxP(v);
if(akt != -1 && !vis[akt]){
q.push(akt);
vis[akt] = 1;
dist[akt] = dist[v] + 1;
}
}
int ans = 1e9;
for(int i = C; i <= D; i++){
ans = min(ans, dist[i]);
}
if(ans == 1e9){
return -1;
}
return ans;
}
