#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(a, b);}
ll lcm(ll a, ll b){return a / gcd(a, b) * b;}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
double cur = rngesus(0, MASK(60) - 1);
cur /= MASK(60) - 1;
return l + cur * (r - l);
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
#include "books.h"
const int INF = 1e9 + 69;
struct SegmentTree{
int n;
vector<int> a;
SegmentTree(int _n){
n = _n;
a.resize(n * 2 + 2, -INF);
}
void update(int i, int v){
i += n; if (!maximize(a[i], v)) return;
while(i > 1){
i >>= 1;
a[i] = max(a[i * 2], a[i * 2 + 1]);
}
}
int get(int l, int r){
l += n; r += n + 1;
int ans = -INF;
while(l < r){
if (l & 1) maximize(ans, a[l++]);
if (r & 1) maximize(ans, a[--r]);
l >>= 1; r >>= 1;
}
return ans;
}
};
ll minimum_walk(vector<int> p, int s) {
int n = p.size();
for(int &i: p) i++;
p.insert(p.begin(), 0);
ll ans = 0;
for(int i = 1; i <= n; ++i){
ans += abs(i - p[i]);
}
vector<pair<int,int>> big_range(n+1, {-1, -1});
for(int i = 1; i <= n; ++i){
if (big_range[i].first != -1) continue;
pair<int,int> mi = {i, i};
int j = p[i];
while(j != i){
minimize(mi.first, j); maximize(mi.second, j);
j = p[j];
}
do{
big_range[j] = mi;
j = p[j];
} while(j != i);
}
SegmentTree mi(n), ma(n);
for(int i = 1; i <= n; ++i) {
mi.update(i, -big_range[i].first);
ma.update(i, big_range[i].second);
}
map<pair<int, int>, ll> dp;
s++;
dp[make_pair(-s, s)] = 0;
while(dp.size()){
auto u = *dp.begin();
dp.erase(dp.begin());
pair<int, int> range = u.first;
ll cost = u.second;
range.first *= -1;
if (range.first == 1 && range.second == n) ans += cost;
pair<int,int> tmp = make_pair(-mi.get(range.first, range.second), ma.get(range.first, range.second));
if (tmp == range){
cost += 2;
if (range.first > 1){
pair<int,int> tmp = {range.first - 1, range.second};
tmp.first *= -1;
if (dp.count(tmp)) minimize(dp[tmp], cost);
else dp[tmp] = cost;
}
if (range.second < n){
pair<int,int> tmp = {range.first, range.second + 1};
tmp.first *= -1;
if (dp.count(tmp)) minimize(dp[tmp], cost);
else dp[tmp] = cost;
}
}
else{
tmp.first *= -1;
if (dp.count(tmp)) minimize(dp[tmp], cost);
else dp[tmp] = cost;
}
}
return ans;
}
// int main(void){
// ios::sync_with_stdio(0);cin.tie(0); cout.tie(0);
// clock_t start = clock();
// int n; cin >> n;
// vector<int> p(n);
// for(int i = 0; i<n; ++i) cin >> p[i];
// int s; cin >> s;
// cout << minimum_walk(p, s) << "\n";
// cerr << "Time elapsed: " << clock() - start << " ms\n";
// return 0;
// }
