#include "railroad.h"
#include <bits/stdc++.h>
#include <bits/extc++.h>
#define StarBurstStream ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define iter(a) a.begin(), a.end()
#define riter(a) a.rbegin(), a.rend()
#define lsort(a) sort(iter(a))
#define gsort(a) sort(riter(a))
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define pf(a) push_front(a)
#define ef(a) emplace_front(a)
#define pob pop_back()
#define pof pop_front()
#define mp(a, b) make_pair(a, b)
#define F first
#define S second
#define mt make_tuple
#define gt(t, i) get<i>(t)
#define tomax(a, b) ((a) = max((a), (b)))
#define tomin(a, b) ((a) = min((a), (b)))
#define topos(a) ((a) = (((a) % MOD + MOD) % MOD))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
#define printv(a, b) {bool pvaspace=false; \
for(auto pva : a){ \
if(pvaspace) b << " "; pvaspace=true;\
b << pva;\
}\
b << "\n";}
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>;
const ll MOD = 1000000007;
const ll MAX = 2147483647;
template<typename A, typename B>
ostream& operator<<(ostream& o, pair<A, B> p){
return o << '(' << p.F << ',' << p.S << ')';
}
ll ifloor(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a < 0) return (a - b + 1) / b;
else return a / b;
}
ll iceil(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a > 0) return (a + b - 1) / b;
else return a / b;
}
vector<int> dsu;
int findDSU(int a){
if(dsu[a] != a) dsu[a] = findDSU(dsu[a]);
return dsu[a];
}
void unionDSU(int a, int b){
a = findDSU(a); b = findDSU(b);
dsu[b] = a;
}
struct info{
int x, id, ty;
};
struct seg{
int id, l, r;
};
long long plan_roller_coaster(vector<int> S, vector<int> T){
int n = (int) S.size();
dsu.resize(n + 1);
iota(iter(dsu), 0);
vector<info> v;
for(int i = 0; i < n; i++){
//cerr << "test " << i << " : " << S[i] << " " << T[i] << "\n";
v.eb(info({S[i], i, 1}));
v.eb(info({T[i], i, 0}));
}
v.eb(info({0, n, 0}));
v.eb(info({1000000001, n, 1}));
sort(iter(v), [&](info x, info y){ return mp(x.x, x.ty) < mp(y.x, y.ty); });
ll ans = 0;
deque<info> lone;
int cnt = 0;
for(info& i : v){
int x = i.x, id = i.id, ty = i.ty;
if(ty == 1){
if(cnt) cnt--;
else lone.eb(i);
continue;
}
if(lone.empty()){
cnt++;
continue;
}
ans += x - lone.front().x;
i.x = lone.front().x;
lone.pof;
}
sort(iter(v), [&](info x, info y){ return mp(x.x, x.ty) < mp(y.x, y.ty); });
vector<int> left;
vector<seg> b;
for(info i : v){
int x = i.x, id = i.id, ty = i.ty;
if(ty == 0){
left.eb(id);
b.eb(seg({id, x, -1}));
continue;
}
int l = left.back();
left.pob;
unionDSU(l, id);
while(b.back().id != l){
unionDSU(b.back().id, id);
b.pob;
}
b.back().r = x;
}
vector<pair<int, pii>> e;
for(int i = 0; i + 1 < (int)b.size(); i++){
if(findDSU(b[i].id) == findDSU(b[i + 1].id)) continue;
e.eb(mp(b[i + 1].l - b[i].r, mp(b[i].id, b[i + 1].id)));
}
lsort(e);
for(auto i : e){
int w = i.F, u = i.S.F, v = i.S.S;
if(findDSU(u) == findDSU(v)) continue;
ans += w;
unionDSU(u, v);
}
return ans;
}
