#include <bits/stdc++.h>
using namespace std;
#define int long long
const int MOD = 1e9+7;
int n,maxh,cate;
int a[500005],b[500005];
int prefmax[500005],suffmax[500005];
int p2[1000005],inv2;
int put(int x, int exp)
{
if(exp==0)
return 1;
if(exp%2==0)
return put(x*x%MOD,exp/2);
else
return put(x*x%MOD,exp/2)*x%MOD;
}
map<int,int> mp,nrm;
int inv[2000005];
int aint[8000005],lazy[8000005];
void build(int nod, int st, int dr)
{
lazy[nod]=1;
if(st==dr)
{
aint[nod] = inv[dr]-inv[st-1];
return;
}
int mij=(st+dr)/2;
build(nod*2,st,mij);
build(nod*2+1,mij+1,dr);
aint[nod] = (aint[nod*2] + aint[nod*2+1])%MOD;
}
void propagate(int nod)
{
if(lazy[nod]==1)
return;
lazy[nod*2] = (lazy[nod*2]*lazy[nod])%MOD;
lazy[nod*2+1] = (lazy[nod*2+1]*lazy[nod])%MOD;
aint[nod*2] = (aint[nod*2]*lazy[nod])%MOD;
aint[nod*2+1] = (aint[nod*2+1]*lazy[nod])%MOD;
lazy[nod]=1;
}
void upd(int nod, int st, int dr, int le, int ri, int newv)
{
assert(newv!=0);
if(le>ri)
return;
if(le==st && dr==ri)
{
lazy[nod] = (lazy[nod]*newv)%MOD;
aint[nod] = (aint[nod]*newv)%MOD;
return;
}
propagate(nod);
int mij=(st+dr)/2;
upd(nod*2,st,mij,le,min(mij,ri),newv);
upd(nod*2+1,mij+1,dr,max(mij+1,le),ri,newv);
aint[nod] = (aint[nod*2] + aint[nod*2+1])%MOD;
}
int qry(int nod, int st, int dr, int le, int ri)
{
if(le>ri)
return 0;
if(le==st && dr==ri)
return aint[nod];
propagate(nod);
int mij=(st+dr)/2;
return (qry(nod*2,st,mij,le,min(mij,ri)) + qry(nod*2+1,mij+1,dr,max(mij+1,le),ri))%MOD;
}
int calc_0(int inc[4][500005])
{
int rez=0;
build(1,1,cate);
for(int i=1;i<=n;i++)
{
rez = (rez + p2[n-i]*qry(1,1,cate,nrm[inc[0][i]],maxh))%MOD;
upd(1,1,cate,nrm[b[i]+1],maxh,2);
}
return rez;
}
int calc_1(int inc[4][500005])
{
int rez=0;
build(1,1,cate);
for(int i=n;i>0;i--)
{
rez = (rez + qry(1,1,cate,nrm[inc[1][i]],maxh)*p2[i-1])%MOD;
upd(1,1,cate,nrm[b[i]+1],maxh,2);
}
return rez;
}
int calc_2(int inc[4][500005])
{
int rez=0;
build(1,1,cate);
for(int i=1;i<=n;i++)
upd(1,1,cate,nrm[b[i]+1],maxh,2);
for(int i=1;i<=n;i++)
{
upd(1,1,cate,nrm[b[i]+1],maxh,inv2);
rez = (rez + qry(1,1,cate,nrm[inc[2][i]],maxh))%MOD;
upd(1,1,cate,nrm[b[i]+1],maxh,2);
}
return rez;
}
int calc_3(int inc[4][500005])
{
int rez=0;
for(int i=1;i<=n;i++)
{
rez = (rez + 5LL*MOD + inv[maxh] - inc[3][i] + 1)%MOD;
}
for(int i=1;i<n;i++)
rez = rez*2%MOD;
return rez;
}
int inc[2][4][500005];
signed main()
{
ios_base::sync_with_stdio(0);cin.tie(0);
p2[0]=1;
for(int i=1;i<=1000000;i++)
p2[i] = p2[i-1]*2%MOD;
inv2 = put(2,MOD-2);
cin>>n;
for(int i=1;i<=n;i++)
cin>>a[i];
for(int i=1;i<=n;i++)
{
cin>>b[i];
if(a[i]>b[i])
swap(a[i],b[i]);
maxh = max(maxh, b[i]);
mp[a[i]]++;
mp[a[i]+1]++;
//mp[b[i]]++;
mp[b[i]+1]++;
}
mp[maxh]++;
mp[0]++;
mp[1]++;
for(auto it:mp)
{
if(!it.second)
continue;
nrm[it.first] = ++cate;
inv[cate] = it.first;
}
maxh = nrm[maxh];
int rez=0;
for(int i=1;i<=n;i++)
prefmax[i] = max(prefmax[i-1], a[i]);
for(int i=n;i>0;i--)
suffmax[i] = max(suffmax[i+1], a[i]);
for(int i=1;i<=n;i++)
{
inc[0][0][i] = inc[1][0][i] = prefmax[i-1]+1;
inc[0][1][i] = inc[1][1][i] = suffmax[i+1]+1;
inc[0][2][i] = inc[1][2][i] = max(prefmax[i-1], suffmax[i+1]) + 1;
inc[0][3][i] = inc[1][3][i] = 0;
for(int j=0;j<4;j++)
{
inc[0][j][i] = max(inc[0][j][i], a[i]+1);
inc[1][j][i] = max(inc[1][j][i], b[i]+1);
}
}
for(int i=0;i<2;i++)
{
rez = (rez + calc_3(inc[i]) + calc_2(inc[i]))%MOD;
rez = (rez + MOD - calc_0(inc[i]))%MOD;
rez = (rez + MOD - calc_1(inc[i]))%MOD;
}
cout<<rez;
return 0;
}
