#include "railroad.h"
#include <bits/stdc++.h>
#define debug printf
#define lp(i,a,b) for(int i = a ; i < b ; i++ )
#define ff first
#define ss second
#define pb push_back
#define mk make_pair
#define ll long long
#define sz size()
#define pii pair<int,int>
#define all(x) x.begin(),x.end()
#define tiii tuple<int,int,int>
#define mkt make_tuple
const int MAXN = 2e5+10 ;
const ll inf = 1e18+10 ;
using namespace std ;
int n , Key , comp ;
int bit[MAXN*2] , realVal[MAXN*2] , myComp[MAXN*2] , pai[MAXN*2] ;
map<int,int> mp ;
vector<int> adj[MAXN*2] ;
ll ans ;
bool vis[MAXN*2] ;
vector< tuple<int,int,int> > edges ;
set<int> thereIsConnection[MAXN*2] ;
void upd(int pos, int val) { for(int i = pos ; i < MAXN*2 ; i += (i&-i) ) bit[i] += val ; }
int qry(int pos)
{
int tot = 0 ;
for(int i = pos ; i > 0 ; i -= (i&-i) )
tot += bit[i] ;
return tot;
}
void dfs(int cur)
{
myComp[cur] = comp ;
vis[cur] = true ;
for(int viz : adj[cur])
if(!vis[viz])
dfs(viz) ;
}
int find(int i)
{
if( pai[i] == i ) return i ;
return pai[i] = find(pai[i]);
}
void join(int a, int b,int cost)
{
a = find(a) ;
b = find(b) ;
if(a == b) return ;
ans += 1LL * cost ;
if( rand()%2 ) pai[a] = b ;
else pai[b] = a ;
}
long long plan_roller_coaster(std::vector<int> s, std::vector<int> t)
{
n = (int)(s.sz);
for(int i : s ) mp[i] = 0 ;
for(int i : t ) mp[i] = 0 ;
for(auto &p : mp )
{
p.ss = ++Key ;
realVal[Key] = p.ff ;
}
int val1,val2;
lp(i,0,n)
{
s[i] = mp[ s[i] ] ;
t[i] = mp[ t[i] ] ;
if( s[i] == t[i] ) continue ;
thereIsConnection[ s[i] ].insert(t[i]) ;
if( s[i] > t[i] )
{
upd( t[i] , -1 ) ;
upd( s[i], 1 ) ;
continue ;
}
upd( s[i] , 1 ) ;
upd( t[i], -1 ) ;
}
upd(1,-1) ;
upd( Key, 1 ) ;
thereIsConnection[Key].insert(1) ;
lp(i,1,Key)
{
int val = qry(i) ;
if(val != 0)
{
thereIsConnection[i].insert(i+1) ;
thereIsConnection[i+1].insert(i) ;
}
if( val > 0 )
ans += 1LL*val*(realVal[i+1]-realVal[i]) ;
}
lp(i,1,Key)
for(auto p : thereIsConnection[i]) adj[i].pb(p) ;
lp(i,1,Key+1)
if( !vis[i] )
{
comp ++ ;
dfs(i) ;
}
lp(i,1,Key)
if( myComp[i] != myComp[i+1] )
edges.pb( mkt( realVal[i+1] - realVal[i] , myComp[i] , myComp[i+1] ) ) ;
sort(all(edges)) ;
lp(i,1,comp+1) pai[i] = i ;
for(auto p : edges)
join( get<1>(p) , get<2>(p) , get<0>(p) ) ;
return ans ;
}
