#include "wiring.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
const int tree_siz = 1024*512-1;
ll drzewo[tree_siz+1];
ll oper[tree_siz+1];
void spych(int v)
{
drzewo[v*2] += oper[v];
drzewo[v*2+1] += oper[v];
oper[v*2] += oper[v];
oper[v*2+1] += oper[v];
oper[v] = 0;
}
void add_seg(int akt, int p1, int p2, int s1, int s2, ll w)
{
if(p2 < s1 || p1 > s2) return;
if(p1 >= s1 && p2 <= s2)
{
drzewo[akt] += w;
oper[akt] += w;
return;
}
spych(akt);
add_seg(akt*2,p1,(p1+p2)/2,s1,s2,w);
add_seg(akt*2+1,(p1+p2)/2+1,p2,s1,s2,w);
drzewo[akt] = min(drzewo[akt*2],drzewo[akt*2+1]);
}
ll get_min(int akt, int p1, int p2, int s1, int s2)
{
if(p2 < s1 || p1 > s2) return 1e15;
if(p1 >= s1 && p2 <= s2)
{
return drzewo[akt];
}
spych(akt);
ll w = min(get_min(akt*2,p1,(p1+p2)/2,s1,s2),get_min(akt*2+1,(p1+p2)/2+1,p2,s1,s2));
return w;
}
ll dp[200'001];
pll arr[200'001];
int prev_same_cnt[200'001];
ll min_total_length(vi r, vi b)
{
vector<pll> e;
forall(it,r)
{
e.pb({it,0});
}
forall(it,b)
{
e.pb({it,1});
}
sort(all(e));
int n = siz(e);
rep(i,n) arr[i+1] = e[i];
add_seg(1,0,tree_siz/2,0,n,1e16);
dp[0] = 0;
int cur_0 = 0;
int cur_1 = 0;
int prev_0 = 0;
int prev_1 = 0;
arr[0].ss = -1;
rep2(i,1,n)
{
dp[i] = 1e18;
if(arr[i].ss == arr[i-1].ss)
{
prev_same_cnt[i] = prev_same_cnt[i-1]+1;
if(arr[i].ss == 1 && prev_0 != 0)
{
if(max(1,prev_0-prev_same_cnt[i]+1) <= prev_0) add_seg(1,0,tree_siz/2,max(1,prev_0-prev_same_cnt[i]+1),prev_0,arr[i].ff - arr[prev_0].ff);
if(prev_0-prev_same_cnt[i] >= prev_0 - prev_same_cnt[prev_0]) add_seg(1,0,tree_siz/2,prev_0 - prev_same_cnt[prev_0],prev_0-prev_same_cnt[i],arr[i].ff - arr[i-prev_same_cnt[i]].ff);
}
if(arr[i].ss == 0 && prev_1 != 0)
{
if(max(1,prev_1-prev_same_cnt[i]+1) <= prev_1) add_seg(1,0,tree_siz/2,max(1,prev_1-prev_same_cnt[i]+1),prev_1,arr[i].ff - arr[prev_1].ff);
if(prev_1-prev_same_cnt[i] >= prev_1 - prev_same_cnt[prev_1]) add_seg(1,0,tree_siz/2,prev_1 - prev_same_cnt[prev_1],prev_1-prev_same_cnt[i],arr[i].ff - arr[i-prev_same_cnt[i]].ff);
}
}
else
{
ll cur_sum = 0;
for(int j = i-1; j >= 1; j--)
{
if(arr[j].ss != arr[i-1].ss) break;
cur_sum += arr[i].ff - arr[j].ff;
add_seg(1,0,tree_siz/2,j,j,-(ll)1e16+cur_sum + dp[j-1]);
}
prev_same_cnt[i] = 0;
}
if(arr[i].ss == 0)
{
if(cur_1 != siz(b))
{
dp[i] = min(dp[i],dp[i-1] + b[cur_1] - arr[i].ff);
}
if(cur_1 != 0)
{
dp[i] = min(dp[i],get_min(1,0,tree_siz/2,prev_1 - prev_same_cnt[prev_1],prev_1));
}
cur_0++;
prev_0 = i;
}
else
{
if(cur_0 != siz(r))
{
dp[i] = min(dp[i],dp[i-1] + r[cur_0] - arr[i].ff);
}
if(cur_0 != 0)
{
dp[i] = min(dp[i],get_min(1,0,tree_siz/2,prev_0 - prev_same_cnt[prev_0],prev_0));
}
cur_1++;
prev_1 = i;
}
}
return dp[n];
}
