#include<bits/stdc++.h>
#define MAXN 1000007
using namespace std;
int n,s,p[MAXN],fr,last,mins,maxs,pref[MAXN],curr;
bool li[MAXN];
long long ans;
int k,cycle[MAXN];
pair<int,int> where[MAXN];
void dfs(int x){
li[x]=true;
cycle[x]=k;
ans+=abs(x-p[x]);
mins=min(mins,x);
maxs=max(maxs,x);
if(!li[p[x]])dfs(p[x]);
}
long long minimum_walk(vector<int> P, int S){
n=int(P.size()); s=S+1;
for(int i=1;i<=n;i++){
p[i]=P[i-1]+1;
}
last=0; fr=n+1;
for(int i=1;i<=n;i++){
if(!li[i]){
if(p[i]!=i)last=i;
dfs(i);
}
}
for(int i=1;i<=n;i++)li[i]=false;
for(int i=n;i>=1;i--){
if(!li[i]){
k++;
if(p[i]!=i)fr=i;
mins=n; maxs=1;
dfs(i);
where[k]={mins,maxs};
pref[mins]++; pref[maxs]--;
}
}
ans/=2;
for(int i=1;i<=n-1;i++){
curr+=pref[i];
if(i<s)continue;
if(curr==0 and last>i)ans+=2;
}
curr=0;
for(int i=n;i>=2;i--){
curr+=pref[i];
if(i>s)continue;
if(curr==0 and fr<i)ans+=2;
}
/// more steps inside initial cycle
vector<int> l,r;
int pt=s;
while(pt<n){
int t=0;
pt=where[cycle[pt]].second+1;
t++;
while(pt<=n and where[cycle[pt]].first>=s){
if(where[cycle[pt]].second==pt){
pt++; t++;
}else{
pt=where[cycle[pt]].second;
}
}
if(pt<=n)r.push_back(t);
}
pt=s;
while(pt>1){
int t=0;
pt=where[cycle[pt]].first-1;
t++;
while(pt>=1 and where[cycle[pt]].second<=s){
if(where[cycle[pt]].first==pt){
pt--; t++;
}else{
pt=where[cycle[pt]].first;
}
}
if(pt>=1)l.push_back(t);
}
if(s!=1)return 0;
for(int i=0;i<l.size();i++){
ans+=min(l[i],r[i]);
}
return ans;
}
/*int main(){
cout<<minimum_walk({12,1,9,3,7,5,6,4,8,2,11,10,0},6)<<"\n";
return 0;
}*/
