#include "books.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define eb emplace_back
#define pb push_back
#define ft first
#define sd second
#define pi pair<int, int>
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define dbg(...) dbg_out(__VA_ARGS__)
using ll = long long;
using ld = long double;
using namespace std;
using namespace __gnu_pbds;
//Constants
const ll INF = 5 * 1e18;
const int IINF = 2 * 1e9;
// const ll MOD = 1e9 + 7;
const ll MOD = 998244353;
const ll dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const ld PI = 3.14159265359;
//Templates
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) {return os << '(' << p.first << ", " << p.second << ')';}
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) {os << '['; string sep; for (const T &x : v) os << sep << x, sep = ", "; return os << ']';}
void dbg_out() {cerr << endl;}
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr << H << ' '; dbg_out(T...); }
template<typename T> void mins(T& x, T y) {x = min(x, y);}
template<typename T> void maxs(T& x, T y) {x = max(x, y);}
template<typename T> using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using omset = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
long long minimum_walk(vector<int> p, int s) {
int n = p.size();
vector<int> min(n, 1 << 30);
vector<int> max(n, -1);
vector<int> col(n, -1);
for (int i = 0, cnt = 0; i < n; i++) {
if (col[i] != -1) {
continue;
}
int u = i;
do {
min[cnt] = std::min(min[cnt], u);
max[cnt] = std::max(max[cnt], u);
col[u] = cnt;
u = p[u];
} while (u != i);
cnt++;
}
int l = 0, r = n - 1;
while (l < s && l == p[l]) {
l++;
}
while (r > s && r == p[r]) {
r--;
}
set<int> st;
for (int i = l; i <= r; i++) {
st.insert(i);
}
int dr = 0;
vector<int> dis(n, 1 << 30);
deque<pi> q;
q.emplace_back(col[s], dis[col[s]] = 0);
while (q.size()) {
int v = q.front().first;
int d = q.front().second;
q.pop_front();
if (d != dis[v]) {
continue;
}
int mn = min[v];
int mx = max[v];
dr = s >= mn && s <= mx ? d : dr;
while (true) {
int u;
auto it = st.lower_bound(mn);
if (it == st.end() || (u = *it) > mx) {
break;
}
st.erase(it);
if (d < dis[col[u]]) {
q.emplace_front(col[u], dis[col[u]] = d);
}
}
if (v < r && d + 1 < dis[col[v + 1]]) {
q.emplace_back(col[v + 1], dis[col[v + 1]] = d + 1);
}
if (v > l && d + 1 < dis[col[v - 1]]) {
q.emplace_back(col[v - 1], dis[col[v - 1]] = d + 1);
}
}
ll ans = 0;
for (int i = l; i <= r; i++) {
ans += abs(i - p[i]);
}
int cnt = 0;
for (int i = l; i <= r; i++) {
dr += !cnt && s < i;
cnt += max[col[i]] == i;
cnt -= min[col[i]] == i;
}
cnt = 0;
for (int i = r; i >= l; i--) {
dr += !cnt && s > i;
cnt += max[col[i]] == i;
cnt -= min[col[i]] == i;
}
return ans + dr * 2;
}
