#include "railroad.h"
#include<bits/stdc++.h>
using namespace std;
const int nmax=2*2e5+42,inf=1e9;
int n;
vector<int> s,t;
int help[nmax],pointer=0;
int pref[nmax];
int parent[nmax];
int root(int node)
{
if(parent[node]==node)return node;
parent[node]=root(parent[node]);
return parent[node];
}
void my_merge(int p,int q)
{
p=root(p);
q=root(q);
parent[p]=q;
}
struct edge
{
int u,v,cost;
};
vector<edge> given;
bool cmp(edge a,edge b)
{
return a.cost<b.cost;
}
long long plan_roller_coaster(vector<int> S, vector<int> T)
{
S.push_back(inf);
T.push_back(1);
n=S.size();
s=S;
t=T;
long long outp=0;
set<int> noted={1,inf};
for(int i=0;i<n;i++)
{
noted.insert(s[i]);
noted.insert(t[i]);
}
for(auto k:noted)
{
pointer++;
help[pointer]=k;
}
for(int i=0;i<=pointer;i++)
{
parent[i]=i;
}
for(int i=0;i<n;i++)
{
int p=lower_bound(help+1,help+pointer+1,s[i])-help;
int q=lower_bound(help+1,help+pointer+1,t[i])-help;
my_merge(p,q);
//cout<<p<<" "<<help[p]<<" "<<q<<" "<<help[q]<<endl;
pref[p]++;
pref[q]--;
}
for(int i=1;i<pointer;i++)
{
pref[i]+=pref[i-1];
//cout<<i<<" -> "<<pref[i]<<" "<<help[i]<<" "<<help[i+1]<<endl;
if(pref[i]>0)
{
outp+=1LL*pref[i]*(help[i+1]-help[i]);
parent[root(i)]=root(i+1);
}
edge cur;
cur.u=i;
cur.v=i+1;
cur.cost=help[i+1]-help[i];
given.push_back(cur);
}
sort(given.begin(),given.end(),cmp);
for(auto k:given)
if(root(k.u)!=root(k.v))
{
outp+=k.cost;
parent[root(k.u)]=root(k.v);
}
return outp;
}
