#include <bits/stdc++.h>
using namespace std;
const long long MOD = (long long)1e9 + 7;
long long binary_expo(long long a, int p) {
  if (p == 0) return 1;
  if (p == 1) return a;
  long long ans = binary_expo(a, p / 2);
  (ans *= ans) %= MOD;
  if (p & 1) (ans *= a) %= MOD;
  return ans;
}
long long inv(long long a) { return binary_expo(a, MOD - 2); }
long long alldiff(pair<int, int> l, pair<int, int> m, pair<int, int> r) {
  long long ans = 1;
  (ans *= (l.second - l.first + 1)) %= MOD;
  (ans *= (m.second - m.first + 1)) %= MOD;
  (ans *= (r.second - r.first + 1)) %= MOD;
  (ans -=
   ((long long)max(0, min(l.second, m.second) - max(l.first, m.first) + 1) *
    (r.second - r.first + 1)) %
   MOD) %= MOD;
  (ans -=
   ((long long)max(0, min(m.second, r.second) - max(m.first, r.first) + 1) *
    (l.second - l.first + 1)) %
   MOD) %= MOD;
  if (ans < 0) ans += MOD;
  (ans += ((long long)max(0, min(l.second, min(m.second, r.second)) -
                                 max(l.first, max(m.first, r.first)) + 1)) %
          MOD) %= MOD;
  (ans *= inv(l.second - l.first + 1)) %= MOD;
  (ans *= inv(m.second - m.first + 1)) %= MOD;
  (ans *= inv(r.second - r.first + 1)) %= MOD;
  (ans *= 2) %= MOD;
  return ans;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<int> l(n), r(n);
  for (int i = 0; i < n; i++) {
    cin >> l[i];
  }
  for (int i = 0; i < n; i++) {
    cin >> r[i];
  }
  for (int i = 0; i < n; i++) {
    if (l[i] > r[i]) {
      cout << 0 << '\n';
      return 0;
    }
  }
  long long tot = 1;
  for (int i = 0; i < n; i++) {
    (tot *= (r[i] - l[i] + 1)) %= MOD;
  }
  long long sum = 1;
  long long squares = 0;
  vector<long long> ind(n);
  for (int i = 0; i < n - 1; i++) {
    long long cur = (long long)(r[i] - l[i] + 1) * (r[i + 1] - l[i + 1] + 1);
    cur %= MOD;
    cur -= max(0, min(r[i], r[i + 1]) - max(l[i], l[i + 1]) + 1);
    if (cur < 0) cur += MOD;
    (cur *= inv(r[i] - l[i] + 1)) %= MOD;
    (cur *= inv(r[i + 1] - l[i + 1] + 1)) %= MOD;
    ind[i] = cur;
    (squares += (cur * cur) % MOD) %= MOD;
    (sum += cur) %= MOD;
  }
  sum = (sum + (sum * sum) % MOD) % MOD - 1;
  sum -= squares;
  if (sum < 0) sum += MOD;
  for (int i = 0; i < n - 2; i++) {
    sum -= 2 * (ind[i] * ind[i + 1]);
    sum %= MOD;
    if (sum < 0) sum += MOD;
    (sum +=
     alldiff({l[i], r[i]}, {l[i + 1], r[i + 1]}, {l[i + 2], r[i + 2]})) %= MOD;
  }
  sum %= MOD;
  cout << sum << '\n';
  return 0;
}
