#include "wiring.h"
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define vi vector<int>
#define pb push_back
#define pii pair<int,int>
#define F first
#define S second
#define REP(i,n) for(int i = 0; i < n; i++)
#define FOR(i,a,b) for(int i = a; i < b; i ++)
#define all(v) v.begin(),v.end()
vector<pii> a;
int n;
int comp[200005];
pii range[200005];
ll dp[200005],pref[200005],suff[200005],gg1[200005],gg2[200005];
ll seg[2][400005];
const ll INF = 1e14;
void upd(int type,int ind,ll val){
ind += n;
while(ind){
seg[type][ind] = min(seg[type][ind],val);
ind /= 2;
}
}
ll quer(int type,int l,int r){
l += n;
r += n;
ll res = INF;
while(l < r){
if(l&1) res = min(res,seg[type][l++]);
if(r&1) res = min(res,seg[type][--r]);
l /= 2;
r /= 2;
}
return res;
}
ll min_total_length(vi r, vi b) {
for(auto x:r) a.pb({x,0});
for(auto x:b) a.pb({x,1});
sort(all(a));
n = a.size();
int last = 0,cmp = 0;
FOR(i,1,n){
if(a[i].S != a[last].S){
range[cmp] = {last,i-1};
last = i;
cmp++;
}
comp[i] = cmp;
}
REP(i,2*n+5) seg[0][i] = seg[1][i] = INF;
range[cmp] = {last,n-1};
pref[0] = 0;
FOR(i,1,n){
if(comp[i] == comp[i-1]){
pref[i] = pref[i-1]+(a[i].F-a[range[comp[i]].F].F);
}
}
suff[n-1] = 0;
for(int i = n-2; i >= 0; i--){
if(comp[i] == comp[i+1]){
suff[i] = suff[i+1]+(a[range[comp[i]].S].F-a[i].F);
}
}
REP(i,n){
if(comp[i]){
int st = range[comp[i]].F;
int l1 = range[comp[st-1]].F,r2 = range[comp[st-1]].S;
ll diff = a[st].F-a[r2].F;
dp[i] = INF;
int r1 = max(2*st-i-1,l1-1);
int l2 = r1+1;
/*
FOR(j,l1,r1+1){
// pref[i]+suff[j]+diff*(st-j)+(j?min(dp[j-1],dp[j]):0)
// [ pref[i]+diff*st ]+[ suff[j]-diff*j+(j?min(dp[j-1],dp[j]):0) ]
// [ pref[i]+diff*st ]+[ gg1[j] ]
dp[i] = min(dp[i],pref[i]+diff*st+gg1[j]);
}
FOR(j,l2,r2+1){
// pref[i]+suff[j]+diff*(i-st+1)+(j?min(dp[j-1],dp[j]):0)
// [ pref[i]+diff*(i-st+1) ]+[ suff[j]+(j?min(dp[j-1],dp[j]):0) ]
// [ pref[i]+diff*(i-st+1) ]+[ gg2[j] ]
dp[i] = min(dp[i],pref[i]+diff*(i-st+1)+gg2[j]);
}
*/
dp[i] = min(pref[i]+diff*st+quer(0,l1,r1+1),pref[i]+diff*(i-st+1)+quer(1,l2,r2+1));
}
else dp[i] = INF;
if(comp[i] == comp[n-1]) continue;
ll diff2 = a[range[comp[i]+1].F].F-a[range[comp[i]].S].F;
gg1[i] = suff[i]-diff2*i+(i?min(dp[i],dp[i-1]):0);
gg2[i] = suff[i]+(i?min(dp[i],dp[i-1]):0);
upd(0,i,gg1[i]);
upd(1,i,gg2[i]);
}
return dp[n-1];
}
