#include "books.h"
#include<iostream>
#include<vector>
#include<queue>
#include<map>
using namespace std;
typedef long long lld;
typedef pair<int,int> state;
typedef std::map<state,lld>::iterator mi;
int arr[1000000];
int n;
int maxa,maxb;
map<state,lld>DP;
lld computevalue(int i, int j){
//cout<<i<<" "<<j<<endl;
if(i<=maxa && maxb<=j)return 0;
mi it=DP.find(state(i,j));
if(it!=DP.end())return it->second;
int start=i;
int end=j;
int ps=start;
int pe=end;
while(pe<=end){
while(ps>=start){
start=min(start,arr[ps]);
end=max(end,arr[ps]);
ps--;
}
start=min(start,arr[pe]);
end=max(end,arr[pe]);
pe++;
}
lld ans=1000000000000000000;
if(start<=maxa && maxb<=end){
DP[state(i,j)]=0;
return 0;
}
if(start>maxa){
ans=min(ans,computevalue(start-1,end)+2);
}
if(end<maxb){
ans=min(ans,computevalue(start,end+1)+2);
}
DP[state(i,j)]=ans;
return ans;
}
lld abs(lld x){
if(x>0)return x;
return -x;
}
long long minimum_walk(std::vector<int> p, int s) {
n=p.size();
for(int i=0;i<n;i++){
arr[i]=p[i];
}
maxa=n;
for(int i=0;i<n;i++){
if(p[i]!=i){
maxa=i;
i=n;
}
}
maxb=-1;
for(int i=n-1;i>-1;i--){
if(p[i]!=i){
maxb=i;
i=-1;
}
}
//cout<<maxa<<" "<<maxb<<endl;
lld ans=0;
for(int i=0;i<n;i++)ans+=abs(p[i]-i);
//cout<<ans<<endl;
ans+=computevalue(s,s);
return ans;
}
