#include <bits/stdc++.h>
#define pb push_back
#define f first
#define sc second
using namespace std;
typedef long long int ll;
typedef string str;
struct dsu{
int n;
vector<int> sz, p;
dsu(int nn){
n = nn;
sz.resize(n, 1);
p.resize(n);
for(int i = 0; i < n; i++) p[i] = i;
}
int get(int x){
if(p[x] != x) p[x] = get(p[x]);
return p[x];
}
void unite(int a, int b){
a = get(a), b = get(b);
if(a == b) return;
if(sz[b] > sz[a]) swap(a, b);
sz[a]+=sz[b];
sz[b] = 0;
p[b] = a;
}
};
ll minimum_walk(vector<int> p, int s){
int n = p.size();
ll ans = 0;
vector<int> C(n, -1), sz;
int k = 0;
for(int i = 0; i < n; i++){
if(C[i] != -1) continue;
int x = p[i];
C[i] = k;
sz.pb(1);
ans+=abs(i-x);
while(x != i){
C[x] = k;
sz.back()++;
ans+=abs(p[x]-x);
x = p[x];
}
k++;
}
//for(int x: C) cerr << x << " "; cerr << "C1\n";
vector<int> first(k, -1), last(k);
for(int i = 0; i < n; i++){
if(first[C[i]] == -1) first[C[i]] = i;
last[C[i]] = i;
}
int L, R;
vector<bool> unnecessary(k, 0);
for(int i = 0; i < n; i++){
if(sz[C[i]] > 1 || i == s){
L = i;
break;
}
unnecessary[C[i]] = 1;
}
for(int i = n-1; i >= 0; i--){
if(sz[C[i]] > 1 || i == s){
R = i;
break;
}
unnecessary[C[i]] = 1;
}
vector<set<int>> sth(k);
for(int i = 0; i < n; i++) sth[C[i]].insert(i);
dsu ds(k);
for(int T = 0; T < k-1; T++){
for(int i = 0; i+1 < n; i++){
if(unnecessary[C[i]] || unnecessary[i+C[1]]) continue;
if(C[i] == C[i+1]) continue;
if(i == last[C[i]] && i+1 == first[C[i+1]]) continue;
auto it = sth[C[i]].find(i);
if(it != sth[C[i]].end() && i+1 == first[C[i+1]] && *next(it) > last[C[i+1]])
continue;
it = sth[C[i+1]].find(i+1);
if(it != sth[C[i+1]].begin() && i == last[C[i]] && *prev(it) < first[C[i]])
continue;
ds.unite(C[i], C[i+1]);
}
for(int &x: C) x = ds.get(x);
first.assign(k, -1);
for(int i = 0; i < n; i++){
if(first[C[i]] == -1) first[C[i]] = i;
last[C[i]] = i;
}
for(int i = 0; i < k; i++){
if(unnecessary[i] || ds.get(i) == i) continue;
int p = ds.get(i);
if(sth[p].size() < sth[i].size()) swap(sth[p], sth[i]);
for(int x: sth[i]) sth[p].insert(x);
sth[i].clear();
}
}
//for(int x: C) cerr << x << " "; cerr << "C2\n";
int l = first[C[s]], r = last[C[s]];
while(l > L || r < R){
int in = -1;
ll lx = 0, rx = 0;
for(int i = l-1; i >= 0; i--){
if(unnecessary[C[i]]) break;
if(C[i] == C[i+1]) continue;
lx+=2;
if(i != last[C[i]]){
in = i;
break;
}
i = first[C[i]];
}
for(int i = r+1; i < n; i++){
if(unnecessary[C[i]]) break;
if(C[i] == C[i-1]) continue;
rx+=2;
if(i != first[C[i]]){
in = i;
break;
}
i = last[C[i]];
}
if(in == -1){
ans+=lx+rx;
break;
}
ans+=min(lx, rx);
l = first[C[in]], r = last[C[in]];
}
return ans;
}
