#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
constexpr int N=4e5+7;
constexpr ll inf=0x3f3f3f3f3f3f3f3f;
void cmin(ll &x,ll y){x=min(x,y);}
int n,a[N],b[N],pos[N];
tuple<int,int,int>h[N];
ll f[N][4];
struct node{
	int trp[4];
	ll trv[4];
	friend node operator +(const node &lhs,const node &rhs){
		node res;
		for(int i=0;i<4;i++)
			res.trp[i]=rhs.trp[lhs.trp[i]],res.trv[i]=lhs.trv[i]+rhs.trv[lhs.trp[i]];
		return res;
	}
}t[N<<2],e{{0,1,2,3},{0,0,0,0}};
int ls(int k){return k<<1;}
int rs(int k){return k<<1|1;}
void pull(int k){t[k]=t[ls(k)]+t[rs(k)];}
void build(int k,int l,int r){
	if(l==r)return t[k]=e,void();
	int mid=(l+r)>>1;
	build(ls(k),l,mid),build(rs(k),mid+1,r);
	return pull(k);
}
void modify(int k,int l,int r,int p,node v){
	if(l==r)return t[k]=v,void();
	int mid=(l+r)>>1;
	if(p<=mid)modify(ls(k),l,mid,p,v);
	else modify(rs(k),mid+1,r,p,v);
	return pull(k);
}
node query(int k,int l,int r,int ql,int qr){
	if(ql<=l&&r<=qr)return t[k];
	int mid=(l+r)>>1;node res=e;
	if(ql<=mid)res=res+query(ls(k),l,mid,ql,qr);
	if(mid<qr)res=res+query(rs(k),mid+1,r,ql,qr);
	return res;
}
int main(){
	cin.tie(nullptr)->sync_with_stdio(false);
	cin>>n;
	for(int i=1;i<=n;i++)cin>>a[i],h[i]={a[i],i,0};
	for(int i=1;i<=n;i++)cin>>b[i],h[n+i]={b[i],i,1};
	sort(h+1,h+2*n+1);build(1,1,2*n);
	memset(f,0x3f,sizeof(f));
	memset(f[0],0,sizeof(f[0]));
	for(int i=1;i<=2*n;i++){
		auto [w,p,tp]=h[i];node cur;
		if(tp)cur=(node){{2,3,0,1},{0,0,w,w}};
		else cur=(node){{1,0,3,2},{0,w,0,w}};
		int k=pos[p];
		pos[p]=i;
		if(k){
			node res=query(1,1,2*n,k+1,i-1)+cur;
			for(int j=0;j<4;j++)cmin(f[i][j],f[i-1][j]),cmin(f[i][res.trp[j]],f[k-1][j]+res.trv[j]);
		}else{
			modify(1,1,2*n,i,cur);
			for(int j=0;j<4;j++)f[i][cur.trp[j]]=f[i-1][j]+cur.trv[j];
		}
	}
	cout<<f[2*n][0]<<'\n';
	return 0;
}