#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<vector<pii>> g;
void init(int dim) { g.resize(dim, vector<pii>()); }
int newnode() { g.emplace_back(); return sz(g) - 1; }
void addedge(int x, int y, int z) {
g[x].emplace_back(y, z);
}
namespace AINT {
int aint[(nmax + nmax / 2) * 2];
void init(int node = 1, int cl = 0, int cr = n - 1) {
if(cl == cr) {
aint[node] = cl;
return;
}
int mid = cl + cr >> 1;
init(2 * node, cl, mid);
init(2 * node + 1, mid + 1, cr);
aint[node] = newnode();
addedge(aint[2 * node], aint[node], 0);
addedge(aint[2 * node + 1], aint[node], 0);
return;
}
void pushto(int val, int l, int r, int node = 1, int cl = 0, int cr = n - 1) {
if(r < cl || cr < l) return;;
if(l <= cl && cr <= r) {
addedge(aint[node], val, 0);
return;
}
int mid = cl + cr >> 1;
pushto(val, l, r, 2 * node, cl, mid);
pushto(val, l, r, 2 * node + 1, mid + 1, cr);
}
}
vector<int> arriv, occ;
vector<int> heap[nmax];
vector<int> dijkstra(int s = -1) {
arriv.resize(sz(g));
occ.resize(sz(g));
for(int i = 0; i <= n + 2; i++) heap[i].clear();
//cerr << sz(arriv) << ' ' << sz(g) << '\n';
fill(all(occ), 0);
if(s != -1) {
fill(all(arriv), inf);
heap[0].emplace_back(s);
arriv[s] = 0;
}
else {
for(int i = 0; i < sz(g); i++)
arriv[i] = min(arriv[i], n + 2),
heap[arriv[i]].emplace_back(i);
}
for(int i = 0; i < n + 2; i++) {
int c = i;
for(int j = 0; j < sz(heap[i]); j++) {
auto node = heap[i][j];
if(occ[node]) continue;
occ[node] = 1;
for(auto [x, e] : g[node]) {
if(arriv[x] > c + e) {
arriv[x] = c + e;
heap[arriv[x]].emplace_back(x);
}
}
}
}
return arriv;
}
}
long long minimum_walk(std::vector<signed> p, signed s) {
n = sz(p);
vector<int> col(n, 0);
vector<int> rs(n + 2, 0), ls(n + 2, 0);
int flag = 0;
ll sum = 0;
G::init(n);
G::AINT::init();
for(int i = 0; i < n; i++) {
if(col[i] == 0 && p[i] != i) {
flag++;
int x = i, cnt = 0;
int L = n;
int R = -1;
while(col[x] != flag) {
col[x] = flag;
L = min(x, L);
R = max(x, R);
sum += abs(x - p[x]);
x = p[x];
cnt++;
}
flag++;
x = i;
int u = G::newnode();
G::AINT::pushto(u, L, R);
while(col[x] != flag) {
col[x] = flag;
G::addedge(u, x, 0);
x = p[x];
}
}
if(i > 0)
G::addedge(i - 1, i, 1),
G::addedge(i, i - 1, 1);
}
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 < sz(G::g); i++) {
G::arriv[i] = fl[i] + fr[i];
}
auto rez = G::dijkstra();
return sum + (ll)rez[s] * 2;
}
#undef int
/**
Anul asta se da centroid.
-- Surse oficiale
*/
