#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
const long long INF = mod;
const long double eps = 1e-8;
long long mod_pow(long long x, long long n) {
  long long ret = 1;
  while (n > 0) {
    if (n % 2) ret = ret * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return ret;
}
void solve() {
  long long n;
  cin >> n;
  vector<long long> l(n), r(n), len(n);
  for (long long i = 0; i < n; i++) cin >> l[i];
  for (long long i = 0; i < n; i++) cin >> r[i];
  for (long long i = 0; i < n; i++) {
    len[i] = (r[i] - l[i] + 1);
  }
  vector<long long> p(n);
  p[0] = 1;
  for (long long i = 0; i < n - 1; i++) {
    long long b = len[i] * len[i + 1] % mod;
    long long le = max(l[i], l[i + 1]);
    long long ri = min(r[i], r[i + 1]);
    long long a = (ri - le + 1);
    if (a < 0) a = 0;
    p[i + 1] = a * mod_pow(b, mod - 2) % mod;
    p[i + 1] = (1 - p[i + 1] + mod) % mod;
  }
  long long ans = 0;
  long long sum = 0;
  for (long long i = 0; i < n; i++) {
    sum += p[i];
    if (sum >= mod) sum -= mod;
  }
  for (long long i = 0; i < n; i++) {
    long long csum = sum;
    if (i - 1 >= 0) csum -= p[i - 1];
    if (i + 1 < n) csum -= p[i + 1];
    csum -= p[i];
    while (csum < 0) csum += mod;
    ans += p[i] * csum % mod;
    if (ans >= mod) ans -= mod;
  }
  ans += sum;
  if (ans >= mod) ans -= mod;
  {
    if (n > 1) {
      ans += 2 * p[1];
      ans %= mod;
    }
  }
  for (long long i = 0; i < n - 2; i++) {
    long long csum = 0;
    long long le = max({l[i], l[i + 1], l[i + 2]});
    long long ri = min({r[i], r[i + 1], r[i + 2]});
    long long a = ri - le + 1;
    if (a < 0) a = 0;
    long long b = len[i] * len[i + 1] % mod * len[i + 2] % mod;
    b = mod_pow(b, mod - 2);
    a = a * b % mod;
    csum += 1 + a - (1 - p[i + 1]) - (1 - p[i + 2]);
    csum = (csum % mod + mod) % mod;
    ans += 2 * csum;
    ans %= mod;
  }
  cout << ans << endl;
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  solve();
  return 0;
}
