#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<bool> vb;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define REP(i,k,n) for(ll i=(ll)(k);i<(ll)(n);i++)
#define all(a) a.begin(),a.end()
#define fi first
#define se second
#define lb(v,k) (lower_bound(all(v),k)-v.bein())
#define dupli(a) {sort(all(a));a.erase(unique(all(a)),a.end());}
#define pb emplace_back
template<class T> bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}
template<class T> bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<class T> void out(T a){cout<<a<<endl;}
template<class T> void outv(T v){rep(i,v.size()){if(i)cout<<' ';cout<<v[i];}cout<<endl;}
const ll inf=1001001001001001001;
long long minimum_walk3(std::vector<int> p, int s) {
ll l=0,r=p.size()-1;
while(l<s&&p[l]==l)l++;
while(r>s&&p[r]==r)r--;
vi v;
REP(i,l,r+1)v.pb(p[i]-l);
s-=l;
ll n=v.size(),ans=0;
rep(i,n-1){
rep(j,i+1)if(v[j]>i)ans++;
}
vvi dp(n,vi(n,inf));
dp[s][s]=0;
for(ll l=s;l>=0;l--){
ll mi=inf,ma=-inf;
REP(r,l,n){
chmax(ma,v[r]);
chmin(mi,v[r]);
if(l)chmin(dp[l-1][r],dp[l][r]+1);
if(r!=n-1)chmin(dp[l][r+1],dp[l][r]+1);
chmin(dp[min(l,mi)][max(r,ma)],dp[l][r]);
}
}
return (ans+dp[0][n-1])*2;
}
long long minimum_walk(std::vector<int> p, int s) {
ll l=0,r=p.size()-1;
while(l<s&&p[l]==l)l++;
while(r>s&&p[r]==r)r--;
vi v;
REP(i,l,r+1)v.pb(p[i]-l);
s-=l;
ll n=v.size(),ans=0;
rep(i,n)ans+=max(0ll,v[i]-i);
deque<ll> deq;
vi dis(n,inf);dis[s]=0;
deq.pb(s);
while(deq.size()){
ll i=deq.front();deq.pop_front();
if(i<s&&chmin(dis[i+1],dis[i]))deq.push_front(i+1);
if(i>s&&chmin(dis[i-1],dis[i]))deq.push_front(i-1);
if(chmin(dis[v[i]],dis[i]))deq.push_front(v[i]);
if(i<n-1&&chmin(dis[i+1],dis[i]+1))deq.pb(i+1);
if(i>0&&chmin(dis[i-1],dis[i]+1))deq.pb(i-1);
}
vi al(1,-1),ar(1,n);
{
ll ma=0;
rep(i,s){
chmax(ma,v[i]);
if(ma==i)al.pb(i);
}
}
{
ll mi=n-1;
for(int i=n-1;i>s;i--){
chmin(mi,v[i]);
if(mi==i)ar.pb(i);
}
}
ans+=al.size()+ar.size()-2;
ans+=dis[al.back()+1];
return ans*2;
}
