#include "railroad.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef tuple<int,int,int> tu;
ll ans;
int p[400010],cross[400010],lv[400010],dis[400010];
vector<int> adj[400010];
vector<tu> v;
set<int> ss;
map<int,int> c;
void dfs(int x, int val) {
p[x]=val;
for (auto s : adj[x]) {
if (p[s]==-1) dfs(s,val);
}
}
int find(int x) {
while (x!=p[x]) x=p[x];
return x;
}
bool same(int x, int y) {
return find(x)==find(y);
}
void unite(int x, int y) {
x=find(x); y=find(y);
if (lv[x]>lv[y]) p[y]=x;
else if (lv[y]>lv[x]) p[x]=y;
else {
p[x]=y; ++lv[y];
}
}
long long plan_roller_coaster(std::vector<int> s, std::vector<int> t) {
int n = (int) s.size();
memset(p,-1,sizeof(p));
for (int i=0; i<n; ++i) {
ss.insert(s[i]);
ss.insert(t[i]);
}
ss.insert(1000000010);
int cnt=0,pre=0;
for (auto it=ss.begin(); it!=ss.end(); ++it) {
if (cnt) v.push_back(tu(*it-pre,cnt,cnt-1)), dis[cnt]=*it-pre;
c[*it]=cnt++;
pre=*it;
}
--cnt;
for (int i=0; i<n; ++i) {
int st=c[s[i]], to=c[t[i]];
if (s[i]<t[i]) {
cross[st+1]++;
cross[to+1]--;
} else if (s[i]>t[i]) {
cross[to+1]--;
cross[st+1]++;
}
adj[st].push_back(to);
}
adj[cnt].push_back(0);
--cross[1];
for (int i=1; i<=cnt; ++i) {
cross[i]+=cross[i-1];
if (cross[i]>0) {
adj[i].push_back(i-1);
ans+=dis[i];
} else if (cross[i]<0) {
adj[i-1].push_back(i);
}
}
for (int i=0; i<=cnt; ++i) {
if (p[i]==-1) dfs(i,i), lv[i]=1;
}
sort(v.begin(),v.end());
for (auto s : v) {
int a,b,w;
tie(w,a,b)=s;
if (!same(a,b)) {
unite(a,b);
ans+=w;
}
}
return ans;
}
