#include <iostream>
#include <fstream>
#include <iomanip>
#include <algorithm>
#include <functional>
#include <numeric>
#include <cstring>
#include <string>
#include <cmath>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <map>
using namespace std;
#define ll long long
#define ull unsigned long long
#define f first
#define s second
#define PF push_front
#define PB push_back
#define MP make_pair
#define max(a, b) ((a > b)? a : b)
#define min(a, b) ((a < b)? a : b)
#define max3(a, b, c) max(max(a, b), c)
#define min3(a, b, c) min(min(a, b), c)
const int N = 2e5 + 5;
const int M = 1e9 + 7;
const int inf = 0x3f3f3f3f;
const ll int INF = 1e18;
struct DSU{
vector<int> parent;
DSU(int n) {
parent = vector<int>(n);
iota(parent.begin(), parent.end(), 0);
}
int find_parent(int p){
return (parent[p] == p)? p : parent[p] = find_parent(parent[p]);
}
bool merge(int a, int b){
a = find_parent(a);
b = find_parent(b);
parent[a] = b;
return (a != b);
}
};
ll int plan_roller_coaster(vector<int> s, vector<int> t){
s.PB(inf);
t.PB(1);
int n = s.size();
// Coordinate Compression
set<int> coor;
for(int i = 0; i < n; i++){
coor.insert(s[i]);
coor.insert(t[i]);
}
map<int, int> mp;
vector<int> val;
int ind = 0;
for(int i : coor){
mp[i] = ind++;
val.PB(i);
}
// Initial connect
DSU dsu(ind);
vector<int> entry(ind, 0);
for(int i = 0; i < n; i++){
entry[mp[s[i]]]++;
entry[mp[t[i]]]--;
dsu.merge(mp[s[i]], mp[t[i]]);
}
vector<int> balance(ind, 0);
for(int i = 0, cur = 0; i < ind; i++){
cur += entry[i];
balance[i] = cur;
}
// Add positive edges
ll int cost = 0;
for(int i = 0; i < ind-1; i++){
if(!balance[i]) continue;
cost += max(0, 1ll * balance[i] * (val[i+1] - val[i]));
dsu.merge(i, i+1);
balance[i] = 0;
}
// Connect unconnected component
using Edge = tuple<int, int, int>;
vector<Edge> edge;
for(int i = 0; i < ind-1; i++){
edge.PB({val[i+1] - val[i], i, i+1});
}
sort(edge.begin(), edge.end());
for(auto [w, i, j] : edge){
if(dsu.merge(i, j)){
cost += w;
}
}
return cost;
}
// int main(){
// ios::sync_with_stdio(false);
// cin.tie(NULL);
// // ifstream cin();
// // ofstream cout();
// ll int temp;
// // temp = plan_roller_coaster({1, 4, 5, 6}, {7, 3, 8, 6});
// // temp = plan_roller_coaster({1, 3, 5, 7}, {2, 4, 6, 8});
// cout << temp << endl;
// }
