#include<bits/stdc++.h>
#include"railroad.h"
#define mp make_pair
#define mt make_tuple
#define all(x) x.begin(), x.end()
#define ff first
#define ss second
using namespace std;
template <typename T>
using matrix = vector<vector<T>>;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
const ll INFL = (1LL<<62)-1;
const int INF = (1<<30)-1;
const double EPS = 1e-7;
const int MOD = 1e9 + 7;
const int RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
const int MAXN = 1e6+1;
struct edge{
ll a, b, w;
bool operator<(edge c) const{
return w < c.w;
}
};
long long plan_roller_coaster(std::vector<int> s, std::vector<int> t) {
int n = s.size();
set<int> S;
S.insert(0);
S.insert(INF);
map<int,int> tr;
for(int i = 0; i < n; i++){
S.insert(s[i]);
S.insert(t[i]);
}
for(int i : S)
tr[i] = tr.size();
int m = tr.size();
vector<int> delta(m);
vector<ll> og(m);
for(pii i : tr){
og[i.ss] = i.ff;
}
for(int& i : s)
i = tr[i];
for(int& i : t)
i = tr[i];
vector<int> pai(m);
iota(all(pai),0);
auto find =[&](int id, auto f){
if(pai[id] == id)
return id;
return pai[id] = f(pai[id],f);
};
auto onion =[&](int a, int b){
a = find(a,find);
b = find(b,find);
if(a == b)
return false;
pai[a] = b;
return true;
};
ll ahead = 1;
ll resp = 0;
for(int i = 0; i < n; i++){
delta[s[i]]--;
delta[t[i]]++;
onion(s[i],t[i]);
}
vector<edge> cand;
for(int i = 0; i < m-1; i++){
ahead+=delta[i];
if(ahead!=0){
resp+=max(0ll,-ahead*(og[i+1]-og[i]));
onion(i,i+1);
} else cand.push_back({i,i+1,og[i+1]-og[i]});
}
sort(all(cand));
for(edge i : cand){
if(onion(i.a,i.b))
resp+=i.w;
}
return resp;
}
