#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define pb push_back
const int MOD = (int)1e9 + 7, INV_2 = (MOD + 1) / 2, LIM = (int)1e9;
int N, glob, a[500005], b[500005], pf_a[500005], sf_a[500005];
int exp_mod(int a, int b) {
int r = 1;
while (b) {
if (b % 2 == 1) {
r = (ll)r * a % MOD;
}
a = (ll)a * a % MOD;
b /= 2;
}
return r;
}
struct node {
node *left, *right;
int val, pv;
node(const int &_s, const int &_e) : left(nullptr), right(nullptr), val(_e - _s + 1), pv(1) {}
void cc(const int &S, const int &E) {
if (left == nullptr) {
int M = (S + E) / 2;
left = new node(S, M);
right = new node(M + 1, E);
}
}
void prop(const int &S, const int &E) {
cc(S, E);
if (pv == 1) {
return;
}
left->val = ((ll)left->val * pv) % MOD;
left->pv = ((ll)left->pv * pv) % MOD;
right->val = ((ll)right->val * pv) % MOD;
right->pv = ((ll)right->pv * pv) % MOD;
pv = 1;
}
void mul(int l, int r, int v, int S = 1, int E = LIM + 1) {
if (l > E || r < S) {
return;
}
if (l <= S && E <= r) {
val = ((ll)val * v) % MOD;
pv = ((ll)pv * v) % MOD;
return;
}
prop(S, E);
int M = (S + E) / 2;
left->mul(l, r, v, S, M);
right->mul(l, r, v, M + 1, E);
val = (left->val + right->val) % MOD;
}
int sum(int l, int r, int S = 1, int E = LIM + 1) {
if (l > E || r < S) {
return 0;
}
if (l <= S && E <= r) {
return val;
}
prop(S, E);
int M = (S + E) / 2;
return (left->sum(l, r, S, M) + right->sum(l, r, M + 1, E)) % MOD;
}
} *root[3];
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
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]);
}
}
root[0] = new node(1, LIM + 1);
root[1] = new node(1, LIM + 1);
root[2] = new node(1, LIM + 1);
for (int i = 1; i <= N; i++) {
root[1]->mul(1, b[i], INV_2);
root[2]->mul(1, b[i], INV_2);
pf_a[i] = max(a[i], pf_a[i - 1]);
}
for (int i = N; i >= 1; i--) {
sf_a[i] = max(a[i], sf_a[i + 1]);
}
for (int i = 1; i <= N; i++) {
root[1]->mul(1, b[i], 2);
root[2]->mul(1, b[i], 2);
for (int h : {a[i], b[i]}) {
int max_p_a = pf_a[i - 1], max_s_a = sf_a[i + 1];
if (max_p_a <= max_s_a) {
glob = (glob + max(0, max_p_a - h)) % MOD;
glob = (glob + max(0, max_s_a - (max(h, max_p_a) + 1) + 1)) % MOD;
glob = (glob - root[0]->sum(max(h, max_p_a) + 1, LIM + 1) + MOD) % MOD;
glob = (glob + max(0, LIM + 1 - (max(h, max_s_a) + 1) + 1)) % MOD;
glob = (glob - root[1]->sum(max(h, max_s_a) + 1, LIM + 1) + MOD) % MOD;
glob = (glob + root[2]->sum(max(h, max_s_a) + 1, LIM + 1)) % MOD;
} else {
glob = (glob + max(0, max_s_a - h)) % MOD;
glob = (glob + max(0, max_p_a - (max(h, max_s_a) + 1) + 1)) % MOD;
glob = (glob - root[1]->sum(max(h, max_s_a) + 1, LIM + 1) + MOD) % MOD;
glob = (glob + max(0, LIM + 1 - (max(h, max_p_a) + 1) + 1)) % MOD;
glob = (glob - root[0]->sum(max(h, max_p_a) + 1, LIM + 1) + MOD) % MOD;
glob = (glob + root[2]->sum(max(h, max_p_a) + 1, LIM + 1)) % MOD;
}
}
root[0]->mul(1, b[i], INV_2);
root[2]->mul(1, b[i], INV_2);
}
for (int rep = 0; rep < N - 1; rep++) {
glob = (glob * 2) % MOD;
}
cout << glob << '\n';
}
