#include "railroad.h"
#include <bits/stdc++.h>
using namespace std;
struct dsu {
vector<int> p;
dsu(int n) : p(n, -1) {}
bool unite(int u, int v) {
if ((u = root(u)) == (v = root(v))) return false;
if (p[u] > p[v]) swap(u, v);
p[u] += p[v];
p[v] = u;
return true;
}
bool same(int u, int v) { return root(u) == root(v); }
int root(int u) { return p[u] < 0 ? u : p[u] = root(p[u]); }
};
long long plan_roller_coaster(std::vector<int> s, std::vector<int> t) {
int n = (int)s.size() + 1;
s.emplace_back(1e9);
t.emplace_back(1);
vector<int> point;
for (int i = 0; i < n; i++) {
point.push_back(s[i]);
point.push_back(t[i]);
}
sort(point.begin(), point.end());
point.erase(unique(point.begin(), point.end()), point.end());
vector<int> a(n), b(n);
for (int i = 0; i < n; i++) {
a[i] = lower_bound(point.begin(), point.end(), s[i]) - point.begin();
b[i] = lower_bound(point.begin(), point.end(), t[i]) - point.begin();
}
int m = point.size();
vector<int> pref(m);
for (int i = 0; i < n; i++) pref[a[i]]++, pref[b[i]]--;
for (int i = 1; i < m; i++) pref[i] += pref[i - 1];
int64_t res = 0;
dsu d(m);
for (int i = 0; i + 1 < m; i++) {
res += 1ll * max(0, pref[i]) * (point[i + 1] - point[i]);
if (pref[i] != 0) d.unite(i, i + 1);
}
for (int i = 0; i < n; i++) d.unite(a[i], b[i]);
vector<tuple<int, int, int>> edges;
for (int i = 0; i + 1 < m; i++) {
edges.emplace_back(point[i + 1] - point[i], i, i + 1);
}
sort(edges.begin(), edges.end());
for (auto [w, u, v] : edges) {
if (d.unite(u, v)) res += w;
}
return res;
}
