// name = railroad_mp_nlogn.cpp, type = cpp.g++
#include "railroad.h"
#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
#define mp make_pair
#define pb push_back
#define fs first
#define sc second
typedef long long int64;
const int INF = (int) 1e9;
int dsu_get(vector<int>& p, int u) {
return (u == p[u]) ? u : (p[u] = dsu_get(p, p[u]));
}
bool dsu_union(vector<int>& p, int u, int v) {
u = dsu_get(p, u), v = dsu_get(p, v);
p[u] = v;
return (u != v);
}
int64 plan_roller_coaster(vector<int> s, vector<int> t) {
int n = (int) s.size();
vector< pair< int, pair< int, int > > > e, edges;
for (int i = 0; i < n; ++i) {
e.pb(mp(s[i], mp(1, i)));
e.pb(mp(t[i], mp(-1, i)));
}
e.pb(mp(INF, mp(1, n)));
e.pb(mp(1, mp(-1, n)));
n++;
vector<int> p(n);
for (int i = 0; i < n; ++i) {
p[i] = i;
}
sort(e.begin(), e.end());
int64 res = 0;
for (int i = 0, delta = 0; i + 1 < (int) e.size(); ++i) {
delta += e[i].sc.fs;
res += max(0, delta) * (int64) (e[i + 1].fs - e[i].fs);
edges.pb(mp(e[i + 1].fs - e[i].fs, mp(e[i].sc.sc, e[i + 1].sc.sc)));
if ((e[i + 1].fs == e[i].fs) || (delta != 0))
dsu_union(p, e[i].sc.sc, e[i + 1].sc.sc);
}
sort(edges.begin(), edges.end());
for (int i = 0; i < (int) edges.size(); ++i)
if (dsu_union(p, edges[i].sc.fs, edges[i].sc.sc))
res += edges[i].fs;
return res;
}
