#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<int, int>
#define f first
#define s second
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) (int)((x).size())
#define pb push_back
#ifdef BALBIT
#define bug(...) cerr<<"#"<<__LINE__<<" "<<#__VA_ARGS__<<": ", _do(__VA_ARGS__)
template <typename T> void _do(T && x) {cerr<<x<<endl;}
template <typename T, typename ...S> void _do(T && x, S&&...y) {cerr<<x<<", "; _do(y...);}
#define IOS()
#else
#define bug(...)
#define IOS() ios::sync_with_stdio(0), cin.tie(0)
#define endl '\n'
#endif
const int maxn = 1e6+5;
bool seen[maxn];
int R[maxn], L[maxn];
bool st[maxn];
bool dv[maxn];
int RR[maxn], LL[maxn];
int par[maxn];
int find(int x) {return x == par[x]? x : par[x] = find(par[x]);}
void mrg(int a, int b) {
a = find(a); b = find(b);
if (a == b) return;
RR[a] = max(RR[a], RR[b]);
LL[a] = min(LL[a], LL[b]);
par[b] = a;
}
vector<int> here[maxn];
ll minimum_walk(vector<int> p, int s) {
memset(seen, 0, sizeof seen);
int n = SZ(p);
ll re= 0;
for (int i = 0; i<n; ++i) {
// --p[i];
re+= abs(i-p[i]);
}
// vector<pair<pii,int> > v;
for (int i = 0; i<n; ++i) {
if (!seen[i]) {
st[i] = 1;
seen[i] = 1;
R[i] = L[i] = i;
for (int x = p[i]; x != i; x = p[x]) seen[x] = 1, R[i] = max(R[i], x);
for (int x = p[i]; x != i; x = p[x]) R[x] = R[i];
bug(i, L[i], R[i]);
LL[i] = L[i]; RR[i] =R[i];
}
}
int nmx = 0;
re -= 2;
for (int i = 0; i<n; ++i) {
nmx = max(nmx, R[i]);
if (nmx <= i) {
re += 2;
dv[i] = 1;
}
// if (i == s && nmx > i) {
// int ad = 0;
// for (int j = 1; ; ++j) {
// if (p[i+j] != i+j || p[i-j] != i-j) {
// ad = j; break;
// }
// }
// bug(ad);
// }
}
for (int i = 0; i<n; ++i) par[i] = i;
vector<pii> stk;
for (int i = 0; i<n; ++i) {
if (st[i]) {
while (!stk.empty() && i > stk.back().s) stk.pop_back();
int newl = i;
while (!stk.empty() && R[i] > stk.back().s) {
mrg(i, stk.back().f);
bug("merged", i, stk.back().f);
newl = stk.back().f;
stk.pop_back();
}
stk.pb({newl, R[i]});
}
}
for (int i = 0; i<n; ++i) {
if (st[i]) {
here[find(i)].pb(i);
for (int x = p[i]; x != i; x = p[x])
here[find(i)].pb(x), par[x] = find(i);
}
}
{
int l= LL[find(s)], r = RR[find(s)];
bug(l,r);
for (int i=l-1; i>=0; --i) {
if (st[i] && RR[find(i)]>r) {
int admn = 10000000;
for (int x : here[find(i)]) {
admn = min(admn, min(abs(l-x), abs(r-x)));
}
re += admn * 2;
l = LL[find(i)]; r = RR[find(i)];
i = l;
}
}
}
for (int i = 0; i<n; ++i) {
if (p[i] == i && i != s) re -= 2;
else break;
}
for (int i = n-1; i>=0; --i) {
if (p[i] == i && i != s) re -= 2;
else break;
}
return re;
}
#ifdef BALBIT
signed main(){
IOS();
bug(minimum_walk({4,3,1,2,0},3));
// bug(minimum_walk({3,2,1,0},0));
// bug(minimum_walk({1,0,3,2},0));
}
#endif
