/*
* File created on 04/08/2022 at 21:58:56.
* Link to problem:
* Description:
* Time complexity: O()
* Space complexity: O()
* Status: ---
* Copyright: Ⓒ 2022 Francois Vogel
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <functional>
using namespace std;
using namespace __gnu_pbds;
#define mp pair<int, pii>
#define pii pair<int, int>
#define f first
#define s second
#define vi vector<int>
#define all(x) x.begin(), x.end()
#define size(x) (int)((x).size())
#define pb push_back
#define ins insert
#define cls clear
#define int ll
#define ll long long
#define ld long double
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
int* par;
int gp(int x) {
return par[x] == x ? x : par[x] = gp(par[x]);
}
void merge(int x, int y) {
x = gp(x);
y = gp(y);
if (x == y) return;
par[y] = x;
}
int plan_roller_coaster_act(vi from, vi to) {
set<int> av;
for (int i : from) av.ins(i);
for (int i : to) av.ins(i);
map<int, int> compress;
int kc = 0;
for (int i : av) compress[i] = kc++;
map<int, int> decompress;
for (auto i : compress) decompress[i.s] = i.f;
for (int i = 0; i < size(from); i++) from[i] = compress[from[i]];
for (int i = 0; i < size(to); i++) to[i] = compress[to[i]];
int n = size(compress);
vi graph [n];
vi revG [n];
for (int i = 0; i < size(from); i++) {
graph[from[i]].pb(to[i]);
revG[to[i]].pb(from[i]);
}
int res = 0;
int sum = 0;
for (int i = 0; i < n-1; i++) {
sum += size(graph[i])-size(revG[i]);
if (sum > 1) {
res += (sum-1LL)*(decompress[i+1]-decompress[i]);
}
for (int j = 1; j > sum; j--) {
sum++;
graph[i].pb(i+1);
revG[i+1].pb(i);
break;
}
for (int j = 1; j < sum; j++) {
sum--;
graph[i+1].pb(i);
revG[i].pb(i+1);
break;
}
}
int comp [n];
for (int i = 0; i < n; i++) comp[i] = -1;
int nbComps = 0;
for (int i = 0; i < n; i++) if (comp[i] == -1) {
queue<int> q;
q.push(i);
comp[i] = nbComps;
while (!q.empty()) {
int x = q.front();
q.pop();
for (int y : graph[x]) if (comp[y] == -1) {
comp[y] = nbComps;
q.push(y);
}
for (int y : revG[x]) if (comp[y] == -1) {
comp[y] = nbComps;
q.push(y);
}
}
nbComps++;
}
vector<mp> edges;
for (int i = 0; i < n-1; i++) if (comp[i] != comp[i+1]) edges.pb(mp(2LL*(decompress[i+1]-decompress[i]), pii(comp[i], comp[i+1])));
sort(all(edges));
par = new int [nbComps];
for (int i = 0; i < nbComps; i++) par[i] = i;
for (auto i : edges) if (gp(i.s.f) != gp(i.s.s)) {
merge(i.s.f, i.s.s);
res += i.f;
}
return res;
}
int plan_roller_coaster(vector<signed> from, vector<signed> to) {
vi ifrom, ito;
for (int i : from) ifrom.pb(i);
for (int i : to) ito.pb(i);
return plan_roller_coaster_act(ifrom, ito);
}
// signed main() {
// cin.tie(0);
// ios_base::sync_with_stdio(0);
// int n;
// cin >> n;
// vector<signed> from(n), to(n);
// for (int i = 0; i < n; i++) cin >> from[i];
// for (int i = 0; i < n; i++) cin >> to[i];
// cout << plan_roller_coaster(from, to) << endl;
// cout.flush();
// int d = 0;
// d++;
// }
