#include "wiring.h"
#include <bits/stdc++.h>
using namespace std;
//macros
typedef long long ll;
typedef pair<int, int> ii;
typedef pair<ll, ll> lll;
typedef tuple<int, int, int> iii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<iii> viii;
typedef vector<ll> vll;
typedef vector<lll> vlll;
#define REP(a,b,c) for(int a=int(b); a<int(c); a++)
#define RE(a,c) REP(a,0,c)
#define RE1(a,c) REP(a,1,c+1)
#define REI(a,b,c) REP(a,b,c+1)
#define REV(a,b,c) for(int a=int(c-1); a>=int(b); a--)
#define INF 1e18
#define pb push_back
#define fi first
#define se second
struct Seg {
Seg() {};
void resize(int size) {
sz = size;
SEG.assign(sz*4, 0);
LAZY.assign(sz*4, 0);
}
void add(int i, int j, ll v, ll lazy=0, int p=0, int l=0, int r=-1) {
if(r == -1) r=sz-1;
SEG [p] += lazy;
LAZY[p] += lazy;
if(j < l || i > r) return;
if(i <= l && j >= r) {
SEG[p] += v;
LAZY[p] += v;
return;
}
int m =(l+r)/2;
add(i,j,v,LAZY[p],p*2+1,l,m);
add(i,j,v,LAZY[p],p*2+2,m+1,r);
SEG[p] = min(SEG[p*2+1], SEG[p*2+2]);
LAZY[p] = 0;
}
void set(int i, ll v, ll lazy=0, int p=0, int l=0, int r=-1) {
if(r == -1) r=sz-1;
SEG [p] += lazy;
LAZY[p] += lazy;
if(i < l || i > r) return;
if(l == r) {
SEG[p] = v;
return;
}
int m=(l+r)/2;
set(i,v,LAZY[p],p*2+1,l,m);
set(i,v,LAZY[p],p*2+2,m+1,r);
SEG[p] = min(SEG[p*2+1], SEG[p*2+2]);
LAZY[p] = 0;
}
ll get(int i, int j, ll lazy=0, int p=0, int l=0, int r=-1) {
if(r == -1) r=sz-1;
SEG [p] += lazy;
LAZY[p] += lazy;
if(j < l || i > r) return INF;
if(i <= l && j >= r) return SEG[p];
int m =(l+r)/2;
ll a=get(i,j,LAZY[p],p*2+1,l,m);
ll b=get(i,j,LAZY[p],p*2+2,m+1,r);
LAZY[p] = 0;
return min(a, b);
}
vll SEG;
vll LAZY;
int sz;
};
const int MX = 6e5;
priority_queue<ii, vii, greater<ii>> pq;
int n[2], p[2], m=0;
vi f[2];
ll a[MX], b[MX], sm[MX];
ll dp[MX], ch[MX];
ll md[MX];
ll ans=0;
Seg seg[2];
ll min_total_length(std::vector<int> R, std::vector<int> B) {
f[0] = R; f[1] = B;
RE(i,2) n[i] = f[i].size();
// fill a and b
RE(i,2) RE(j,n[i]) pq.push({f[i][j], i});
while(!pq.empty()) {
a[m] = pq.top().fi;
b[m] = pq.top().se;
pq.pop(); m++;
}
ch[0]=0; md[0]=0; sm[0]=0;
REP(i,1,m) {
md[i] = md[i-1];
ch[i] = ch[i-1];
sm[i] = sm[i-1] + a[i-1];
if(b[i] != b[i-1]) ch[i]++, md[i]=i;
}
sm[m] = sm[m-1]+a[m-1];
dp[0] = 0;
RE(i,2) seg[i].resize(m+2);
REP(i,1,m+1) {
ll ed = i-1;
ll mid = md[ed];
ll bg = md[max(0ll,mid-1)];
if(mid == ed) {
REI(j,bg,mid) RE(k,2) seg[k].set(j,dp[j]);
REP(i,bg,mid) RE(k,2) seg[k].add(bg,i,-a[i]);
REP(j,bg,mid) seg[0].add(j,j,-a[mid ]*j);
REP(j,bg,mid) seg[1].add(j,j,-a[mid-1]*j);
}
dp[i] = INF;
if(mid == 0) continue;
ll switchJ = 2*mid-ed-1;
REV(j,bg,mid+1) {
ll cost = 0;
ll left = mid-j;
ll right = ed-mid+1;
REP(i,mid,ed+1) cost += a[i];
if(j < switchJ) {
cost += a[mid ]*switchJ;
dp[i] = min(dp[i], seg[0].get(j,j) + cost);
} else {
cost += a[mid-1]*switchJ;
dp[i] = min(dp[i], seg[1].get(j,j) + cost);
}
}
}
return dp[m];
}
