#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <iomanip>
#include <array>
#include <string>
#include <algorithm>
#include <cmath>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <bitset>
#include <list>
#include <iterator>
#include <numeric>
#include <complex>
#include <utility>
#include <random>
#include <cassert>
#include <fstream>
using namespace std;
mt19937 rnd(time(nullptr));
/* -------------------- Typedefs -------------------- */
typedef int itn;
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
typedef float fl;
typedef long double ld;
/* -------------------- Usings -------------------- */
using vi = vector<int>;
using vll = vector<ll>;
using mii = map<int, int>;
using mll = map<ll, ll>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
/* -------------------- Defines -------------------- */
#define ff first
#define ss second
#define pub push_back
#define pob pop_back
#define puf push_front
#define pof pop_front
#define mpr make_pair
#define yes cout<<"Yes\n"
#define no cout<<"No\n"
#define all(x) (x).begin(), (x).end()
#define USACO freopen("feast.in", "r", stdin); freopen("feast.out", "w", stdout);
/* -------------------- Constants -------------------- */
const int dx[8] = { -1, 0, 1, 0, -1, -1, 1, 1 };
const int dy[8] = { 0, -1, 0, 1, -1, 1, -1, 1 };
const int MAX = int(1e9 + 5);
const ll MAXL = ll(2e18) + 5ll;
const ll MOD = ll(1000000007);
const ll MOD2 = ll(998244353);
/* -------------------- Functions -------------------- */
void fastio() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
}
void precision(int x) {
cout.setf(ios::fixed | ios::showpoint);
cout.precision(x);
}
ll gcd(ll a, ll b) {
if (a == 0 || b == 0) return 0;
while (b) {
a %= b;
swap(a, b);
}
return a;
}
ll lcm(ll a, ll b) {
return a / gcd(a, b) * b;
}
ll range_sum(ll a, ll b) {
if (a > b) return 0ll;
ll dif = a - 1, cnt = b - a + 1;
ll ans = ((b - a + 1) * (b - a + 2)) / 2;
ans += ((b - a + 1) * dif);
return ans;
}
string dec_to_bin(ll a) {
string s = "";
for (ll i = a; i > 0; ) {
ll k = i % 2;
i /= 2;
char c = k + 48;
s += c;
}
if (a == 0) {
s = "0";
}
reverse(all(s));
return s;
}
ll bin_to_dec(string s) {
ll num = 0;
for (int i = 0; i < s.size(); i++) {
num *= 2ll;
num += (s[i] - '0');
}
return num;
}
ll factorial_by_mod(ll n, ll mod) {
ll ans = 1;
ll num;
for (ll i = 1; i <= n; ++i) {
num = i % mod;
ans *= num;
ans %= mod;
}
return ans;
}
bool isPrime(ll a) {
if (a == 1) return false;
for (ll i = 2; i * i <= a; i++) {
if (a % i == 0) return false;
}
return true;
}
ll binpow(ll a, ll b) {
if (!a) return 0;
ll ans = 1;
while (b) {
if (b & 1) {
ans *= a;
}
b >>= 1;
a *= a;
}
return ans;
}
ll binpow_by_mod(ll a, ll b, ll mod) {
if (!a) return 0;
ll ans = 1;
while (b) {
if (b & 1) {
ans *= a;
ans %= mod;
}
b >>= 1;
a *= a;
a %= mod;
}
return ans;
}
/* -------------------- Solution -------------------- */
const int INV2 = (MOD + 1) / 2;
struct SegTree {
struct Node { int prod, sum; };
int n;
vector<Node> st;
SegTree(int N, int initVal = 0) : n(N), st(4 * N) {
build(1, 0, n - 1, initVal);
}
static Node merge(const Node& L, const Node& R) {
Node res;
res.prod = int((1LL * L.prod * R.prod) % MOD);
res.sum = (L.sum + 1LL * L.prod * R.sum) % MOD;
return res;
}
void build(int p, int l, int r, int val) {
if (l == r) { st[p] = { val, val }; return; }
int m = (l + r) >> 1;
build(p << 1, l, m, val);
build(p << 1 | 1, m + 1, r, val);
st[p] = merge(st[p << 1], st[p << 1 | 1]);
}
void update(int idx, int val) { update(1, 0, n - 1, idx, val); }
void update(int p, int l, int r, int idx, int val) {
if (l == r) { st[p] = { val, val }; return; }
int m = (l + r) >> 1;
if (idx <= m) update(p << 1, l, m, idx, val);
else update(p << 1 | 1, m + 1, r, idx, val);
st[p] = merge(st[p << 1], st[p << 1 | 1]);
}
int prod() const { return st[1].prod; }
int sum() const { return st[1].sum; }
};
/* ---------- fast exponentiation ---------- */
long long mod_pow(long long a, long long e = 0, long long m = MOD) {
long long res = 1;
while (e) {
if (e & 1) res = res * a % m;
a = a * a % m;
e >>= 1;
}
return res;
}
struct Event {
long long h;
int idx;
int val;
bool operator<(const Event& o) const { return h < o.h; }
};
void slv() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N;
cin >> N;
vector<long long> a(N), b(N);
for (auto& x : a) cin >> x;
for (auto& x : b) cin >> x;
vector<Event> ev;
ev.reserve(2 * N);
for (int i = 0; i < N; ++i) {
long long mn = min(a[i], b[i]);
long long mx = max(a[i], b[i]);
ev.push_back({ mn + 1, i, INV2 });
ev.push_back({ mx + 1, i, 1 });
}
sort(ev.begin(), ev.end());
SegTree st(N, 0), stR(N, 0);
long long prevH = 1;
long long answer = 0;
size_t pos = 0;
const int Nmod = N % MOD;
while (pos < ev.size()) {
long long h = ev[pos].h;
long long len = h - prevH;
if (len) {
int sumPref = st.sum();
int sumSuf = stR.sum();
int prodTot = st.prod();
int S = (((Nmod - sumPref - sumSuf) % MOD + MOD) % MOD
+ int(1LL * Nmod * prodTot % MOD)) % MOD;
answer = (answer + (len % MOD) * 1LL % MOD * S) % MOD;
}
while (pos < ev.size() && ev[pos].h == h) {
int idx = ev[pos].idx;
int val = ev[pos].val;
st.update(idx, val);
stR.update(N - 1 - idx, val);
++pos;
}
prevH = h;
}
long long sumHeights = 0;
for (int i = 0; i < N; ++i)
sumHeights = (sumHeights + (a[i] + b[i]) % MOD) % MOD;
sumHeights = sumHeights * 1LL * INV2 % MOD;
long long expectedWater = (answer - sumHeights + MOD) % MOD;
long long result = expectedWater * mod_pow(2, N) % MOD;
cout << result << '\n';
}
void cs() {
int tstc = 1;
//cin >> tstc;
while (tstc--) {
slv();
}
}
void precalc() {
return;
}
int main() {
fastio();
precalc();
//precision(0);
cs();
return 0;
}
