#include <bits/stdc++.h>
#define all(x) (x).begin(),(x).end()
using namespace std;
using ll = long long;
using ld = long double;
//#define int ll
#define sz(x) ((int)(x).size())
using pii = pair<int,int>;
using tii = tuple<int,int,int>;
const int nmax = 1e6 + 5, inf = 1e9 + 5;
int n;
namespace G {
vector<pii> g[nmax];
void addedge(int x, int y, int z) {
g[x].emplace_back(y, z);
}
priority_queue<pii, vector<pii>, greater<pii>> heap;
vector<int> arriv, occ;
vector<int> dijkstra(int s = -1) {
arriv.resize(n);
occ.resize(n);
fill(all(occ), 0);
if(s != -1) {
fill(all(arriv), inf);
heap.emplace(0, s);
arriv[s] = 0;
}
else {
for(int i = 0; i < n; i++)
heap.emplace(arriv[i], i);
}
while(!heap.empty()) {
auto [c, node] = heap.top();
heap.pop();
if(occ[node]) continue;
occ[node] = 1;
for(auto [x, e] : g[node]) {
if(arriv[x] > c + e) {
arriv[x] = c + e;
heap.emplace(arriv[x], x);
}
}
}
return arriv;
}
}
long long minimum_walk(std::vector<int> p, int s) {
n = sz(p);
vector<int> col(n, 0);
vector<int> rs(n + 2, 0), ls(n + 2, 0);
int flag = 0;
multiset<int> lhf;
ll sum = 0;
for(int i = 0; i < n; i++) {
if(col[i] == 0) {
flag++;
int x = i, cnt = 0;
set<int> vals;
while(col[x] != flag) {
col[x] = flag;
sum += abs(x - p[x]);
x = p[x];
cnt++;
vals.emplace(x);
}
int L = *vals.begin();
int R = *vals.rbegin();
flag++;
x = i;
while(col[x] != flag) {
col[x] = flag;
G::addedge(L, x, 0);
G::addedge(R, x, 0);
x = p[x];
}
}
if(i > 0)
G::addedge(i - 1, i, 2),
G::addedge(i, i - 1, 2);
}
int sl = 0, sr = n - 1;
while(p[sl] == sl && sl < s) sl++;
while(p[sr] == sr && sr > s) sr--;
auto fl = G::dijkstra(sl), fr = G::dijkstra(sr);
for(int i = 0; i < n; i++) {
G::arriv[i] = fl[i] + fr[i];
}
auto rez = G::dijkstra();
return sum + rez[s];
}
/**
Anul asta se da centroid.
-- Surse oficiale
*/
