#include "books.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
const ll MOD = 998244353;
const ll INF = 1e18;
const ld EPS = 1e-12;
#define endl "\n"
#define sp <<" "<<
#define REP(i, a, b) for(ll i = a; i < b; i++)
#define dbg(x) cout << #x << " = " << x << endl
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define fast_io() ios_base::sync_with_stdio(false); cin.tie(NULL)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((ll)(x).size())
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
// http://xorshift.di.unimi.it/splitmix64.c
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
template <typename Key, typename Value>
using hash_map = unordered_map<Key, Value, custom_hash>;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
// uniform_int_distribution<int>(a, b)(rng);
// shuffle(all(a), rng);
ll minimum_walk(vector<int> p, int s) {
assert(s == 0);
int n = p.size();
int last = 0;
ll ans = 0;
vector<int> pos(n);
REP(i, 0, n) {
pos[p[i]] = i;
}
vector<bool> vis(n, false);
vector<pair<pair<int, int>, int>> sub;
auto touch = [&](int i) -> void {
int ele = p[i], loc = i;
// check overflow later
int curr = 2LL * loc;
int l = n+1, r = -1;
while (loc != ele and !vis[ele]) {
curr += abs(loc - ele);
vis[ele] = true;
loc = ele, ele = p[loc];
l = min(l, ele), r = max(r, ele);
}
sub.push_back({{l, r}, curr});
ans += curr;
};
REP(i, 0, n) {
if (!vis[i] and p[i] != i) {
touch(i);
}
}
sort(all(sub));
// for (auto &x : sub) {
// cerr << "(" << x.fi.fi << ", " << x.fi.se << " - " << x.se << "), ";
// } cerr << endl;
for (auto &x : sub) {
if (x.fi.fi <= last) {
ans -= 2LL * x.fi.fi;
} else {
ans -= 2LL * last;
}
last = max(last, x.fi.se);
}
return ans;
}
// int main() {
// vector<int> wow = {0, 1, 2, 3};
// do {
// REP(i, 0, 4) cerr << wow[i] << " ";
// cerr << endl;
// cerr << minimum_walk(wow, 0) << endl;
// } while (next_permutation(all(wow)));
// return 0;
// }
