#include "books.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
#define mk make_pair
#define pb push_back
#define fr first
#define sc second
ll minimum_walk(vector<int> p, int s) {
int n = sz(p), L = n, R = -1;
vector<int> l(n), r(n);
vector<bool> vis(n,0);
vector<pii> aux, range;
ll ans = 0;
for(int i = 0; i < n; i++) {
int x = i, m = i;
vector<int> cicle;
while(!vis[x]) {
vis[x] = 1;
cicle.pb(x);
x = p[x];
m = max(m, x);
}
for(int it : cicle) l[it] = i, r[it] = m;
ans += abs(p[i]-i);
aux.pb({i,m});
if(i != m or i == s) L = min(L,i), R = max(R,m);
}
for(int i = 0; i < sz(aux);) {
int l = aux[i].fr, r = aux[i].sc, j = i;
while(j < sz(aux) and aux[j].fr <= r) {
r = max(r, aux[j].sc);
j++;
}
i=j;
range.pb({l,r});
}
for(int i = 1; i < sz(range); i++)
if(range[i-1].fr >= L and range[i].sc <= R)
ans += 2*(range[i].fr - range[i-1].sc);
vector<pii> a(n), b(n);
for(int i = 1; i < n; i++) {
if(l[i-1] <= l[i]) {
a[i] = mk(i-1, max(0,l[i] - i + 1));
continue;
}
a[i].fr = a[i-1].fr;
while(l[a[i].fr] > l[i]) a[i].fr = a[a[i].fr].fr;
a[i].sc = max(0, l[i] - a[i].fr);
}
b[n-1] = mk(n-1,0);
for(int i = n-2; i >= 0; i--) {
if(r[i+1] >= r[i]) {
b[i] = mk(i+1, max(0,i+1 - r[i]));
continue;
}
b[i].fr = b[i+1].fr;
while(r[b[i].fr] < r[i]) b[i].fr = b[b[i].fr].fr;
b[i].sc = max(0, b[i].fr - r[i]);
}
vector<int> dist(n, n);
deque<int> fila;
fila.emplace_front(s);
dist[s] = 0;
vis.clear();
vis.resize(n,0);
while(!fila.empty()) {
int x = fila.front();
fila.pop_front();
if(vis[x]) continue;
vis[x] = 1;
if(dist[a[x].fr] > dist[x] + a[x].sc) {
if(a[x].sc == 0) fila.emplace_front(a[x].fr);
else fila.emplace_back(a[x].fr);
dist[a[x].fr] = dist[x] + a[x].sc;
}
if(dist[b[x].fr] > dist[x] + b[x].sc) {
if(b[x].sc == 0) fila.emplace_front(b[x].fr);
else fila.emplace_back(b[x].fr);
dist[b[x].fr] = dist[x] + b[x].sc;
}
}
for(int i = 0; i < sz(range); i++)
if(range[i].sc >= s) { R = range[i].sc; break; }
return ans + 2*dist[R];
}
