#include "books.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
const int maxn = 1e6 + 5, INF = 1e9;
int p[maxn];
int vis[maxn];
bool taken[maxn];
vector<pair<int,int>> vec = {{-1, -1}};
int l, r;
void expand(int L, int R) {
vector<int> add;
while (l > L) {
l--;
if (p[l]!=l) add.push_back(vis[l]);
}
while (r<R) {
r++;
if (p[r]!=r) add.push_back(vis[r]);
}
for (int i:add) expand(vec[i].first, vec[i].second);
}
int minimum_walk(vector<int32_t> P, int32_t s) {
int n = P.size();
for (int i=0;i<n;i++) p[i] = P[i];
for (int i=0;i<n;i++) vis[i] = false;
int ans = 0;
int cnt = 0;
for (int i=0;i<n;i++) if (!vis[i]) {
if (p[i]==i && i==s) {
cnt++;
vis[i] = cnt;
vec.push_back({s, s});
}
if (p[i]==i) continue;
int u = i;
pair<int,int> val = {u, u};
cnt++;
while (true) {
vis[u] = cnt;
val.first = min(u, val.first);
val.second = max(u, val.second);
int v = p[u];
ans += abs(v-u);
if (v==i) break;
u = v;
}
vec.push_back(val);
}
l = s, r = s;
expand(vec[vis[s]].first, vec[vis[s]].second);
bool done = false;
while (l>0 || r<n-1) {
for (int dist = 1; ; dist++) {
int L = l-dist, R = r + dist;
if (L<0 && R>=n) {done = true; break;}
if (L>=0 && p[L]!=L) {
ans += dist*2;
expand(L, r);
break;
}
if (R<n && p[R]!=R) {
ans += dist*2;
expand(l, R);
break;
}
}
if (done) break;
}
return ans;
}
