#include "books.h"
#define N 1000005
#define f first
#define ss second
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
ll ans = 0;
ll n, maior[N], menor[N], qtd = 0, ok[N], en;
int pai[N], peso[N];
int find(int x)
{
if(x == pai[x]) return x;
return pai[x] = find(pai[x]);
}
void join(int a, int b)
{
a = find(a), b = find(b);
if(a == b) return;
if(peso[a] > peso[b]) pai[b] = a;
else if(peso[a] < peso[b]) pai[a] = b;
else pai[a] = b, peso[b] ++;
}
vector<int> g;
void dfs(ll x, ll &mx, ll &mn)
{
mx = max(mx, maior[x]);
if(ok[x]) return;
ok[x] = 1;
dfs(g[x], mx, mn);
}
ll minimum_walk(vector<int> p, int s)
{
n = p.size();
g = p;
for(ll i = 0; i < n; i++) ans += abs(i - p[i]);
for(int i = 0; i < n; i++) maior[i] = menor[i] = i;
for(ll i = n - 1; i >= 0; i--)
{
if(p[i] != i)
{
en = i;
break;
}
}
vector<pii> sweep;
for(int i = 0; i <= en; i++)
{
if(ok[i]) continue;
dfs(i, maior[i], menor[i]);
sweep.push_back({menor[i], maior[i]});
}
sort(sweep.begin(), sweep.end());
for(int i = 0; i < (int)sweep.size(); i++) pai[i] = i;
pii a = {-1, -1};
for(int i = 0; i < (int)sweep.size(); i++)
{
auto b = sweep[i];
if(b.f <= a.f) join(i, a.ss);
a = max(a, {b.ss, i});
//for(int j = 0; j < i; j++)
//{
//}
}
set<int> q;
for(int i = 0; i < (int)sweep.size(); i++)
{
q.insert(find(i));
}
ll qtd = q.size();
//cout<<q.size()<<"\n";
return ans + 2*(qtd - 1);
}
