#include <bits/stdc++.h>
using namespace std;
long long n;
long long l[200005], r[200005];
const long long mod = 1e9 + 7;
long long x[200005];
long long s[200005];
long long ME(long long x, long long nn, long long M) {
  long long result = 1;
  while (nn > 0) {
    if (nn % 2 == 1) result = (result * x) % M;
    x = (x * x) % M;
    nn = nn / 2;
  }
  return result;
}
long long inv(long long x) { return ME(x, mod - 2, mod); }
long long f(long long i) {
  long long L = max(max(l[i], l[i + 1]), l[i + 2]);
  long long R = min(min(r[i], r[i + 1]), r[i + 2]);
  if (L > R) return 0;
  long long ret = ((R - L + 1) * inv(r[i] - l[i] + 1)) % mod;
  ret = (ret * inv(r[i + 1] - l[i + 1] + 1)) % mod;
  ret = (ret * inv(r[i + 2] - l[i + 2] + 1)) % mod;
  return ret;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n;
  for (long long i = 1; i <= n; i++) {
    cin >> l[i];
  }
  for (long long i = 1; i <= n; i++) cin >> r[i];
  long long ans = 0;
  ans = (n * n) % mod;
  for (long long i = n - 1; i >= 1; i--) {
    s[i] = s[i + 1];
    long long L = max(l[i], l[i + 1]);
    long long R = min(r[i], r[i + 1]);
    if (L > R) {
      continue;
    } else {
      x[i] = ((R - L + 1) * inv(r[i] - l[i] + 1)) % mod;
      x[i] = (x[i] * inv(r[i + 1] - l[i + 1] + 1)) % mod;
    }
    s[i] = (s[i] + x[i]) % mod;
  }
  ans = (ans + s[1]) % mod;
  ans = (ans - (2 * n * s[1]) % mod + mod) % mod;
  for (long long i = n - 2; i >= 1; i--) {
    long long ret = (x[i] * s[i + 2]) % mod;
    ret = (ret + f(i)) % mod;
    ans = (ans + ret + ret) % mod;
  }
  cout << ans << endl;
  return 0;
}
