#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]);
}
int dp[1007][1007];
bool vis[1007][1007];
int ff(int l,int r){
if(l==1 and r==n)return 0;
if(vis[l][r])return dp[l][r];
vis[l][r]=true;
if(l>1){
int from=l-1,to=r,ll=l-1,rr=r+1;
while(ll>=from or rr<=to){
while(ll>=from){
from=min(from,where[cycle[ll]].first);
to=max(to,where[cycle[ll]].second);
ll--;
}
while(rr<=to){
from=min(from,where[cycle[rr]].first);
to=max(to,where[cycle[rr]].second);
rr++;
}
}
dp[l][r]=min(dp[l][r],ff(from,to)+1);
}
if(l>1){
int from=l,to=r+1,ll=l-1,rr=r+1;
while(ll>=from or rr<=to){
while(ll>=from){
from=min(from,where[cycle[ll]].first);
to=max(to,where[cycle[ll]].second);
ll--;
}
while(rr<=to){
from=min(from,where[cycle[rr]].first);
to=max(to,where[cycle[rr]].second);
rr++;
}
}
dp[l][r]=min(dp[l][r],ff(from,to)+1);
}
return dp[l][r];
}
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;
li[i]=false; pref[i]=0;
}
last=0; fr=n+1; k=0; ans=0;
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;
/// more steps inside initial cycle
if(s!=1)ans+=ff(s,s);
else{
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;
}
}
return ans;
}
/*int main(){
vector<int> perm;
for(int i=0;i<10;i++){
perm.push_back(i);
}
while(true){
random_shuffle(perm.begin(),perm.end());
for(int i=0;i<10;i++){
cout<<perm[i]<<" ";
}
cout<<"\n";
int z=rand()%10;
cout<<z<<"\n";
minimum_walk(perm,z);
}
return 0;
}*/
