#include "books.h"
#include <vector>
#include <algorithm>
#include <cmath>
#include <cassert>
#include <cstdio>
using namespace std;
bool visit[1000100];
vector<pair<int,int>> uni(vector<pair<int,int>> &tbl) {
sort(tbl.begin(),tbl.end(),[](const pair<int,int> &a,const pair<int,int> &b) {
if (a.second!=b.second) return a.second<b.second;
return a.first<b.first;
});
vector<pair<int,int>> re;
for (int i=0;i<(int)tbl.size();i++) {
int curl=tbl[i].first;
while (!re.empty()&&tbl[i].first<=re.back().second) {
curl=min(curl,re.back().first);
re.pop_back();
}
re.push_back({curl,tbl[i].second});
}
return re;
}
vector<pair<pair<int,int>,pair<int,int>>> rem(vector<pair<pair<int,int>,pair<int,int>>> &tbl,vector<pair<int,int>> &out,bool &excess) {
excess=false;
sort(tbl.begin(),tbl.end(),[](const pair<pair<int,int>,pair<int,int>> &a,const pair<pair<int,int>,pair<int,int>> &b) {
if (a.first.second!=b.first.second) return a.first.second<b.first.second;
return a.first.first>b.first.first;
});
vector<pair<pair<int,int>,pair<int,int>>> re;
for (int i=0;i<(int)tbl.size();i++) {
while (!re.empty()&&tbl[i].first.first<=re.back().first.first) {
excess=true;
out.push_back(re.back().first);
re.pop_back();
}
re.push_back(tbl[i]);
}
return re;
}
long long minimum_walk(vector<int> p, int s) {
int n=(int)p.size();
vector<pair<int,int>> coord;
vector<pair<int,int>> nonover;
vector<pair<pair<int,int>,pair<int,int>>> over;
long long ans=0;
int globl=-1e9;
int globr=1e9;
for (int i=0;i<n;i++) {
if (visit[i]) continue;
visit[i]=true;
int mn=i;
int mx=i;
int cl=-1e9;
int cr=1e9;
if (i<=s) cl=max(cl,i);
if (i>=s) cr=min(cr,i);
int cur=p[i];
ans+=abs(p[i]-i);
while (cur!=i) {
visit[cur]=true;
mx=max(mx,cur);
mn=min(mn,cur);
if (cur<=s) cl=max(cl,cur);
if (cur>=s) cr=min(cr,cur);
ans+=abs(p[cur]-cur);
cur=p[cur];
}
if (mn==mx) continue;
globl=max(globl,cl);
globr=min(globr,cr);
coord.push_back({mn,mx});
if (mn>=s||mx<=s) nonover.push_back({mn,mx});
else over.push_back({{mn,mx},{cl,cr}});
}
coord.push_back({s,s});
auto re=uni(coord);
for (int i=1;i<(int)re.size();i++) {
ans+=(re[i].first-re[i-1].second)*2;
}
if (over.empty()) {
return ans;
}
//-------------------------------------------
bool excess;
auto over2=rem(over,nonover,excess);
if (excess) {
ans+=min(s-globl,globr-s);
}
int ll=-1e9;
int rr=1e9;
for (auto &i:over2) {
ll=max(ll,i.second.first);
rr=min(rr,i.second.second);
}
nonover.push_back({ll,ll});
nonover.push_back({rr,rr});
nonover.push_back({s,s});
auto nonover2=uni(nonover);
long long addr=0;
bool stflag=false;
for (int i=0;i<(int)nonover2.size();i++) {
if (nonover2[i].first<=s&&s<=nonover2[i].second) {
stflag=true;
if (nonover2[i].first<=rr&&rr<=nonover2[i].second) break;
continue;
}
if (!stflag) continue;
addr+=(nonover2[i].first-nonover2[i-1].second)*2;
if (nonover2[i].first<=rr&&rr<=nonover2[i].second) break;
}
stflag=false;
long long addl=0;
for (int i=(int)nonover2.size()-1;i>=0;i--) {
if (nonover2[i].first<=s&&s<=nonover2[i].second) {
stflag=true;
if (nonover2[i].first<=ll&&ll<=nonover2[i].second) break;
continue;
}
if (!stflag) continue;
addl+=(nonover2[i+1].first-nonover2[i].second)*2;
if (nonover2[i].first<=ll&&ll<=nonover2[i].second) break;
}
ans+=min(addl,addr);
return ans;
}
