#include "railroad.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const int MAXN = 4e5+5;
#define all(x) x.begin(), x.end()
#define mk make_pair
#define pb push_back
#define fr first
#define sc second
int pai[MAXN], sz[MAXN];
int find(int x) {
if(x == pai[x]) return x;
return pai[x] = find(pai[x]);
}
void join(int x, int y) {
x = find(x);
y = find(y);
if(x == y) return;
if(sz[x] <= sz[y]) {
pai[x] = y;
sz[y] += sz[x];
}
else {
pai[y] = x;
sz[x] += sz[y];
}
}
ll plan_roller_coaster(vector<int> s, vector<int> t) {
map<int,int> corr;
set<int> numbers;
vector<int> vel;
for(int i = 0; i < (int)s.size(); i++)
numbers.insert(s[i]), numbers.insert(t[i]);
for(auto it : numbers) {
corr[it] = vel.size();
vel.pb(it);
}
// corr[num] = pos
// vel[pos] = num
int n = vel.size();
vector<int> in(n), out(n);
for(int i = 0; i < n; i++)
pai[i] = i, sz[i] = 1;
for(int i = 0; i < (int)s.size(); i++) {
int u = corr[s[i]], v = corr[t[i]];
out[u]++;
in[v]++;
join(u,v);
}
join(0, n-1);
in[0]++;
out[n-1]++;
ll ans = 0;
vector<pii> edges;
for(int i = 0; i < n-1; i++) {
if(out[i] - in[i] > 0) {
ans += (ll)(vel[i+1]-vel[i])*(ll)(out[i]-in[i]);
out[i+1] += (out[i] - in[i]);
in[i] = out[i];
join(i, i+1);
}
else if(out[i] - in[i] < 0) {
in[i+1] += in[i] - out[i];
out[i] = in[i];
join(i, i+1);
}
edges.pb({vel[i+1]-vel[i], i});
}
sort(all(edges));
for(auto [cost, u] : edges) {
if(find(u) != find(u+1))
join(u,u+1), ans += cost;
}
return ans;
}
