#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
const int N = 200005;
long long inv(long long n) {
  if (n == 1) return 1;
  return (mod - mod / n) * inv(mod % n) % mod;
}
long long l[N], r[N];
inline long long compute2(int i) {
  long long lo = max(l[i - 1], l[i]);
  long long hi = min(r[i - 1], r[i]);
  if (lo > hi) return 0;
  long long tmp = (hi - lo + 1) * inv(r[i] - l[i] + 1) % mod;
  (tmp *= inv(r[i - 1] - l[i - 1] + 1)) %= mod;
  return tmp % mod;
}
inline long long compute3(int i) {
  long long lo = max({l[i - 2], l[i - 1], l[i]});
  long long hi = min({r[i - 2], r[i - 1], r[i]});
  if (lo > hi) return 0;
  long long tmp = (hi - lo + 1) * inv(r[i] - l[i] + 1) % mod;
  (tmp *= inv(r[i - 1] - l[i - 1] + 1)) %= mod;
  (tmp *= inv(r[i - 2] - l[i - 2] + 1)) %= mod;
  return tmp % mod;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cout << setprecision(32);
  int n;
  cin >> n;
  if (n == 1) {
    cout << 1 << '\n';
    exit(0);
  }
  for (int i = 1; i <= n; i++) {
    cin >> l[i];
  }
  for (int i = 1; i <= n; i++) {
    cin >> r[i];
  }
  long long ans = 1;
  for (int i = 2; i <= n; i++) {
    ans += 3 * (mod + 1 - compute2(i));
  }
  ans %= mod;
  long long sum = 0;
  for (int i = 4; i <= n; i++) {
    sum += mod + 1 - compute2(i - 2);
    sum %= mod;
    ans += 2 * (mod + 1 - compute2(i)) * sum % mod;
    ans %= mod;
  }
  for (int i = 3; i <= n; i++) {
    ans += 2 * (1 + mod * 2 - compute2(i) - compute2(i - 1) + compute3(i));
  }
  ans %= mod;
  cout << ans << endl;
  return 0;
}
