#include "books.h"
#include <bits/stdc++.h>
using namespace std;
#define pii pair<int,int>
#define ll long long
const int mxn = 1e6+10;
const int LEN = mxn*20;
int N;
int nid[LEN],to[LEN],wei[LEN],head[LEN];
int d1[LEN],d2[LEN];
ll ans = 0;
bitset<LEN> vis;
int ecnt,vcnt;
int seg[mxn*4];
void add_edge(int a,int b,int w){
//cerr<<"ADD_EDGE: "<<a<<' '<<b<<' '<<w<<endl;
ecnt++;
nid[ecnt] = head[a];
head[a] = ecnt;
to[ecnt] = b;
wei[ecnt] = w;
return;
}
void build(int now,int l,int r){
if(l == r){
seg[now] = l;
return;
}
seg[now] = vcnt++;
int mid = (l+r)>>1;
build(now*2+1,l,mid);
build(now*2+2,mid+1,r);
add_edge(seg[now*2+1],seg[now],0);
add_edge(seg[now*2+2],seg[now],0);
//cerr<<l<<' '<<r<<"::"<<seg[now]<<":"<<seg[now*2+1]<<' '<<seg[now*2+2]<<endl;
return;
}
void add(int now,int l,int r,int s,int e,int p){
if(l>=s&&e>=r){
//cerr<<l<<' '<<r<<":"<<p<<endl;
add_edge(seg[now],p,0);
return;
}
int mid = (l+r)>>1;
if(mid>=s)add(now*2+1,l,mid,s,e,p);
if(mid<e)add(now*2+2,mid+1,r,s,e,p);
return;
}
priority_queue<pii,vector<pii>,greater<pii>> pq;
void DIJKSTRA(int dist[]){
vis.reset();
for(int i = 0;i<vcnt;i++)pq.push(pii(dist[i],i));
while(!pq.empty()){
auto [d,now] = pq.top();
pq.pop();
if(vis[now])continue;
vis[now] = true;
for(int eid = head[now];eid;eid = nid[eid]){
int nxt = to[eid],w = wei[eid];
if(dist[nxt]>dist[now]+w){
dist[nxt] = dist[now]+w;
pq.push(pii(dist[nxt],nxt));
}
}
}
return;
}
long long minimum_walk(std::vector<int> p, int s) {
N = p.size();
vcnt = N;
for(int i = 0;i+1<N;i++){
add_edge(i,i+1,1);
add_edge(i+1,i,1);
}
build(0,0,N-1);
for(int i = 0;i<p.size();i++){
ans += abs(i-p[i]);
if(vis[i])continue;
int now = i;
int lp = i,rp = i;
do{
lp = min(lp,now);
rp = max(rp,now);
vis[now] = true;
now = p[now];
}while(now != i);
int tar = vcnt++;
add(0,0,N-1,lp,rp,tar);
do{
add_edge(tar,now,0);
now = p[now];
}while(now != i);
}
fill(d1,d1+LEN,LEN);
fill(d2,d2+LEN,LEN);
int tl = s,tr = s;
for(int i = 0;i<N;i++){
if(p[i] != i)tl = min(tl,i),tr = max(tr,i);
}
//cerr<<tl<<','<<tr<<endl;
d1[tl] = d2[tr] = 0;
DIJKSTRA(d1);
DIJKSTRA(d2);
//for(int i = 0;i<vcnt;i++)cerr<<d1[i]<<' ';cerr<<endl;
//for(int i = 0;i<vcnt;i++)cerr<<d2[i]<<' ';cerr<<endl;
for(int i = 0;i<vcnt;i++)d1[i] += d2[i];
DIJKSTRA(d1);
//for(int i = 0;i<vcnt;i++)cerr<<d1[i]<<' ';cerr<<endl;
return ans+d1[s]*2;
}
