#include <bits/stdc++.h>
#include "railroad.h"
using ll = long long;
using std::vector;
using std::array;
using std::pair;
using std::tuple;
int dedup(vector<int>& v) {
std::sort(v.begin(), v.end());
v.erase(std::unique(v.begin(), v.end()), v.end());
return v.size();
}
int lowb(const vector<int>& v, const int x) {
return std::lower_bound(v.begin(), v.end(), x) - v.begin();
}
struct union_find {
vector<int> par;
explicit union_find(const int n) : par(n, -1) {}
int find(const int u) {
return par[u] < 0 ? u : par[u] = find(par[u]);
}
bool merge(int x, int y) {
x = find(x), y = find(y);
if (x == y) return false;
if (par[x] > par[y]) std::swap(x, y);
par[x] += par[y];
par[y] = x;
return true;
}
};
ll plan_roller_coaster(vector<int> s, vector<int> t) {
const int n = s.size();
vector<int> cx;
cx.reserve(2 * n + 2);
cx.push_back(0);
cx.push_back(1000000001);
std::copy(s.begin(), s.end(), std::back_inserter(cx));
std::copy(t.begin(), t.end(), std::back_inserter(cx));
const int m = dedup(cx);
vector<int> coeff(m);
coeff[0] -= 1;
coeff[m - 1] += 1;
union_find dsu(m);
for (int i = 0; i < n; ++i) {
const int a = lowb(cx, s[i]);
const int b = lowb(cx, t[i]);
coeff[a] += 1;
coeff[b] -= 1;
dsu.merge(a, b);
}
ll cur = 0, ret = 0;
vector<tuple<int, int, int>> edge;
for (int i = 0; i < m; ++i) {
if (i > 0) {
if (cur != 0) dsu.merge(i - 1, i);
if (cur > 0) ret += cur * (cx[i] - cx[i - 1]);
edge.emplace_back(cx[i] - cx[i - 1], i - 1, i);
}
cur += coeff[i];
}
std::sort(edge.begin(), edge.end());
for (const auto& [c, u, v] : edge) {
if (dsu.merge(u, v)) {
ret += c;
}
}
return ret;
}
