#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define all(x) x.begin(),x.end()
#define pb push_back
#define for1(i,x,n) for(int i=x;i<=n;i++)
#define for2(i,x,n) for(int i=x;i>=n;i--)
#define int ll
typedef long long ll;
typedef pair<int,int> pii;
const ll maxn=2e5+69;
const ll mod=1e9+7;
const ll inf=1e18;
int n,a[maxn],b[maxn];
int mu2[maxn],chia2;
namespace sub2
{
void sol()
{
int res=0;
for1(i,1,n)
{
res+=mu2[n-1]+mod*2-mu2[i-1]-mu2[n-i]+1;
res%=mod;
}
cout << res;
}
}
namespace sub1
{
int x[50],pre[50],suf[50];
void sol()
{
int ans=0;
for1(mask,0,(1<<n)-1)
{
for1(i,1,n)
{
if ((mask>>(i-1))&1) x[i]=a[i];
else x[i]=b[i];
}
for1(i,1,n) pre[i]=max(pre[i-1],x[i]);
for2(i,n,1) suf[i]=max(suf[i+1],x[i]);
for1(i,1,n)
{
ans+=min(pre[i],suf[i])-x[i];
ans%=mod;
}
}
cout << ans;
}
}
namespace sub23
{
int f[1001]; // fi la so truong hop ma i la gia tri lon nhat, gi=fi*i
int res[10001];
void Update(int i)
{
int x=0;
for1(j,0,b[i]) x+=f[j];
f[b[i]]+=x;
f[b[i]]%=mod;
x=0;
for1(j,0,a[i]-1) x+=f[j],f[j]=0;
f[a[i]]+=x;
f[a[i]]%=mod;
for1(j,b[i]+1,1000) f[j]=f[j]*2%mod;
}
int Get(int x)
{
int r1=0,r2=0,res=0;
for1(i,b[x]+1,1000)
{
r1+=f[i];
// if (x==1 && i!=0) cerr<< i<<'\n';
r2+=f[i]*i%mod;
}
r1=(r1%mod)*chia2%mod;
r2=(r2%mod)*chia2%mod;
res=r2+mod-(r1*b[x]%mod);
res%=mod;
int fb=f[b[x]];
for1(i,a[x],b[x]-1)
{
fb-=f[i];
r1+=f[i];
r2+=f[i]*i%mod;
}
fb%=mod;
if (fb<0) fb+=mod;
fb=fb*chia2%mod;
r1+=fb;
r2+=fb*b[x]%mod;
r1%=mod;
r2%=mod;
res+=r2+mod-(r1*a[x]%mod);
// if (x==1) cerr<< res<<'\n';
return res%mod;
}
void sol()
{
f[0]=1;
for1(i,1,n)
{
Update(i);
res[i]=Get(i)*mu2[n-i]%mod;
}
for1(i,0,1000)f[i]=0;
f[0]=1;
for2(i,n,1)
{
Update(i);
res[i]=(res[i]+ (Get(i)*mu2[i-1]%mod))%mod;
}
int ans=0;
for1(i,1,n)
{
ans=ans+res[i]+mod-Get(i);
ans%=mod;
}
cout << ans;
}
}
void sol()
{
// cerr<< pw(2,mod-2);
chia2=500000004;
cin >> n;
for1(i,1,n) cin >> a[i];
bool is_sub2=1;
mu2[0]=1;
for1(i,1,n) mu2[i]=mu2[i-1]*2%mod;
for1(i,1,n)
{
cin >> b[i];
if (b[i]<a[i]) swap(a[i],b[i]);
if (a[i]!=1 || b[i]!=2) is_sub2=0;
}
if (is_sub2)
{
sub2::sol();
return;
}
if (n<=20)
{
sub1::sol();
return;
}
if (n<=1e4)
{
sub23::sol();
return;
}
}
int32_t main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
// freopen("wall.inp","r",stdin);
// freopen("wall.out","w",stdout);
int t=1;//cin >> t;
while (t--)
{
sol();
}
}
/*
10
1 2 3 4 5 6 7 8 9 10
10 9 8 7 6 5 4 3 2 1
*/
