#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
slope trick solution
knew the solution idea beforehand
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "wiring.h"
struct SlopeTrick{
ll l,r,dir;
ll first_pos,first_val;
priority_queue<ll,vector<ll>,greater<ll>> pq;
SlopeTrick(ll l_, ll r_, ll dir_){
l = l_, r = r_, dir = dir_;
if(dir == 1) first_pos = l;
else first_pos = r;
first_val = inf2;
}
void min_conv(vector<pair<ll,ll>> v){
if(l == r){
for(auto [x,y] : v){
if(x == 0){
first_val += y;
}
}
return;
}
if(first_val >= inf2) return;
if(dir == 1){
pq.push(v[1].ss-v[0].ss);
first_val += v[0].ss;
first_pos += v[0].ff;
while(first_pos < l){
first_val += pq.top();
pq.pop();
first_pos++;
}
}
else{
pq.push(v[0].ss-v[1].ss);
first_val += v[1].ss;
first_pos += v[1].ff;
while(first_pos > r){
first_val += pq.top();
pq.pop();
first_pos--;
}
}
}
void upd(ll x){
if(x > first_val) return;
ll sub = first_val-x;
first_val = x;
if(!pq.empty()){
ll mn = pq.top();
pq.pop();
pq.push(mn+sub);
}
}
};
long long min_total_length(std::vector<int> a, std::vector<int> b) {
ll n = sz(a), m = sz(b);
sort(all(a)), sort(all(b));
vector<array<ll,3>> c;
rep(i,n){
ll x = a[i];
auto it = lower_bound(all(b),x);
ll bef = -inf2, aft = inf2;
if(it != b.end()) aft = *it;
if(it != b.begin()) bef = *prev(it);
ll mn_dis = min(abs(x-bef),abs(x-aft));
c.pb({x,mn_dis,1});
}
rep(i,m){
ll x = b[i];
auto it = lower_bound(all(a),x);
ll bef = -inf2, aft = inf2;
if(it != a.end()) aft = *it;
if(it != a.begin()) bef = *prev(it);
ll mn_dis = min(abs(x-bef),abs(x-aft));
c.pb({x,mn_dis,2});
}
sort(all(c));
SlopeTrick small(-inf1,-1,-1), med(0,0,1), big(1,inf1,1);
med.upd(0);
for(auto [x,y,t] : c){
if(t == 1){
// red
// small: min conv with (0,y),(1,x)
// med: min conv with (0,y),(1,-x)
// big: min conv with (0,y),(1,-x)
ll small_to_med = small.first_val+x;
ll med_to_big = med.first_val-x;
small.min_conv({{0,y},{1,x}});
med.min_conv({{0,y},{1,-x}});
big.min_conv({{0,y},{1,-x}});
med.upd(small_to_med);
big.upd(med_to_big);
}
else{
// blue
// small: min conv with (-1,-x),(0,y)
// med: min conv with (-1,-x),(0,y)
// big: min conv with (-1,x),(0,y)
ll big_to_med = big.first_val+x;
ll med_to_small = med.first_val-x;
small.min_conv({{-1,-x},{0,y}});
med.min_conv({{-1,-x},{0,y}});
big.min_conv({{-1,x},{0,y}});
med.upd(big_to_med);
small.upd(med_to_small);
}
// vector<ll> v;
// auto curr = big.pq;
// while(!curr.empty()){
// v.pb(curr.top());
// curr.pop();
// }
// debug(big.first_val);
// debug(v);
// debug(small.first_val);
// debug(med.first_val);
// debug(big.first_val);
// cout << endl;
}
ll ans = med.first_val;
ll oans = -1;
// {
// ll siz = sz(c);
// c.insert(c.begin(),{0,0});
// vector<ll> p(siz+5), pref(siz+5);
// rep1(i,siz){
// p[i] = p[i-1], pref[i] = pref[i-1];
// if(c[i][2] == 1) p[i]++, pref[i] += c[i][0];
// else p[i]--, pref[i] -= c[i][0];
// }
// vector<ll> dp(siz+5,inf2);
// vector<ll> prev_occ(2*siz+5,-1);
// dp[0] = 0;
// prev_occ[siz] = 0;
// rep1(i,siz){
// dp[i] = dp[i-1]+c[i][1];
// if(prev_occ[p[i]+siz] != -1){
// ll j = prev_occ[p[i]+siz];
// ll diff = pref[i]-pref[j];
// amin(dp[i],dp[j]+abs(diff));
// }
// prev_occ[p[i]+siz] = i;
// }
// oans = dp[siz];
// }
// debug(ans,oans);
// assert(ans == oans);
return ans;
}
