#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#define pb push_back
#define F first
#define S second
#define all(a) a.begin(),a.end()
#define pii pair <int,int>
#define PII pair<pii , pii>
#define ld long double
#define int long long
#define sz(v) (int)v.size()
#define rep(i , a , b) for(int i=a;i <= b;i++)
#define per(i, a , b) for(int i=a;i >= b;i--)
using namespace std ;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int maxn = 5e5 + 10 , N = 1e5 +1 , lg = 20 , maxq = 202 , sq = 333 , inf = 2e9 +100 , maxk = 2022 , mod = 1e9 + 7 ;
int n , s[28*maxn] , a2 , lz[28*maxn] , a[maxn] , b[maxn] , pr[maxn] , sf[maxn] , ans =0 ;
vector <int> cm ;
int po(int a, int b){
if(b==0)return 1;
int v= po(a,b/2);
v= v*v % mod ;
if(b&1) v = v*a % mod ;
return v;
}
void shi(int p){
int pl = p<<1 ,pr =p<<1|1;
s[pl] = s[pl] * lz[p] % mod ;
s[pr] = s[pr] * lz[p]%mod ;
lz[pl] = lz[pl] * lz[p] % mod ;
lz[pr] = lz[pr] * lz[p] % mod ;
lz[p] = 1;
}
void bui(int p =1 ,int l = 0 , int r =sz(cm)-2){
int mid = (l+r)/2 , pl = p<<1 , pr = p<<1|1 ;
if(l == r){
s[p] =cm[l+1]-cm[l] ;
lz[p] =1 ;
return ;
}
bui(pl,l,mid);
bui(pr,mid+1 , r);
s[p] = (s[pl] + s[pr])%mod ;
lz[p] =1 ;
}
void upd(int le ,int ri ,int w ,int p = 1, int l = 0 , int r =sz(cm)-2){
int mid = (l+r) /2 , pl =p<<1,pr=p<<1|1 ;
if(le > r || l > ri)return ;
if(l!=r)shi(p) ;
if(le <= l && r <= ri){
s[p] = (s[p] * w)%mod ;
lz[p] = lz[p] * w % mod ;
return ;
}
upd(le,ri,w,pl,l,mid);
upd(le,ri,w,pr,mid+1,r) ;
s[p] = (s[pl] + s[pr])%mod ;
lz[p] =1 ;
}
int que(int le ,int ri , int p =1 ,int l = 0 , int r =sz(cm)-2){
int mid = (l+r)/2 , pl = p<<1 ,pr = p<<1|1 ;
if(le > r || l > ri)return 0 ;
if(l!=r)shi(p) ;
if(le <= l &&r <= ri)return s[p] ;
return (que(le ,ri ,pl,l,mid) + que(le , ri ,pr ,mid+1 , r))%mod ;
}
vector <pair<pii , int> > v1[maxn] , v2[maxn] , v3[maxn] ;
void sl(int i , int l ,int r, int w){
int x = min(pr[i-1] , sf[i+1]) , y = max(pr[i-1] ,sf[i+1] )+1 ;
ans = (ans + max(0ll , min(x,r)-l+1) * w)%mod ;
l = max(l , x+1) ;
if(l > r)return ;
y = max(y, l);
if(r >= y){
cm.pb(y);cm.pb(r+1) ;
ans = (ans + (r-y+1)*w)%mod ;
v3[i].pb({{y,r+1},w});
v2[i].pb({{y,r+1},(-w+mod)%mod}) ;
v1[i].pb({{y,r+1},(-w+mod)%mod}) ;
}
r = min(r,y-1);
if(l > r)return ;
cm.pb(l);cm.pb(r+1);
ans = (ans + (r-l+1)*w)%mod ;
if(pr[i-1] > sf[i+1]){
v2[i].pb({{l,r+1},(-w+mod)%mod});
}else{
v1[i].pb({{l,r+1},(-w+mod)%mod});
}
}
int f(int x){
int y = lower_bound(all(cm) , x) - cm.begin() ;
return y ;
}
signed main() {
ios::sync_with_stdio(false); cin.tie(0);
a2 = po(2, mod-2) ;
cin >> n ;
rep(i , 1,n){
cin >> a[i] ;
}
rep(i , 1 ,n){
cin >> b[i] ;
if(a[i] > b[i])swap(a[i] , b[i]) ;
}
pr[0] = -inf ;
rep(i ,1 ,n){
pr[i] = max(pr[i-1] , a[i]) ;
}
sf[n+1] = -inf ;
per(i , n ,1 ){
sf[i] = max(sf[i+1] , a[i]) ;
cm.pb(a[i]+1);cm.pb(b[i]+1) ;
}
rep(i ,2 , n-1){
sl(i,a[i] + 1, b[i] , a2) ;
sl(i,b[i] +1 , 1e9 , 1) ;
}
sort(all(cm)) ;
cm.resize(unique(all(cm)) - cm.begin()) ;
bui() ;
rep(i ,1 , n){
for(auto [x, w] : v1[i]){
x.F = f(x.F) ;
x.S = f(x.S) ;
ans = (ans + w * que(x.F,x.S-1))%mod ;
}
upd(f(a[i]+1) ,f(b[i]+1)-1 , a2) ;
}
rep(i , 1 , n){
upd(f(a[i]+1) , f(b[i]+1)-1 , 2) ;
for(auto [x, w] : v3[i]){
x.F = f(x.F) ;
x.S = f(x.S) ;
ans = (ans + w * que(x.F,x.S-1))%mod ;
}
upd(f(a[i]+1) , f(b[i]+1)-1 , a2) ;
}
bui() ;
per(i , n ,1 ){
for(auto [x, w] : v2[i]){
x.F = f(x.F) ;
x.S = f(x.S) ;
ans = (ans + w * que(x.F,x.S-1))%mod ;
}
upd(f(a[i]+1) ,f(b[i]+1)-1 , a2) ;
}
cout <<ans*po(2,n)%mod << "\n" ;
}
/*
*/
