#include "books.h"
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define fi first
#define se second
#define sz(a) (int)(a.size())
#define all(a) a.begin(),a.end()
typedef long long int ll;
typedef pair<int,int> pii;
const int MAXN = 1e6+1;
int par[MAXN];
int find(int x){
if(x==par[x])return x;
return par[x] = find(par[x]);
}
ll minimum_walk(vector<int> p, int s) {
int n = sz(p);
ll ans = 0;
for(int i=0;i<n;i++){
ans+=abs(i-p[i]);
par[i] = i;
}
for(int i=0;i<n;i++){
if(i==p[i])continue;
int mn = min(i,p[i]);
int mx = max(i,p[i]);
int j = mn;
while(find(j)+1 <= mx){
j = find(j);
par[j] = j+1;
}
}
vector<pii>lf,rg;
pii md = {-1,-1};
for(int i=0;i<n;i++){
if(i==p[i])continue;
int j = i;
while(j+1<n && find(i) == find(j+1))j++;
if(j<=s)lf.pb({i,j});
else if(i>=s)rg.pb({i,j});
else md = {i,j};
i = j;
}
ll add = 0;
if(md.fi != -1){
add+=min(s-md.fi,md.se-s);
lf.pb({md.fi,md.fi});
rg.insert(rg.begin(),{md.se,md.se});
}else{
lf.pb({s,s});
rg.insert(rg.begin(),{s,s});
}
//for(pii x:lf)cout<<x.fi<<" "<<x.se<<'\n';
//cout<<add<<'\n';
for(int i=0;i+1<sz(lf);i++)add+=lf[i+1].fi - lf[i].se;
//cout<<add<<'\n';
for(int i=0;i+1<sz(rg);i++)add+=rg[i+1].fi - rg[i].se;
//cout<<add<<'\n';
ans+=2*add;
return ans;
}
