#include <bits/stdc++.h>
using namespace std;
long long n, l[200005], r[200005], med, num, var, covar, p[200005],
    mod = 1e9 + 7ll, x, y, z, a, b, c, tmpl, tmpr, tot;
long long fastp(long long base, long long exp) {
  if (exp == 0) return 1ll;
  long long tmp = fastp(base, exp / 2);
  tmp = (tmp * tmp) % mod;
  if (exp % 2) tmp *= base;
  return tmp % mod;
}
inline long long inv(long long x) { return fastp(x, mod - 2ll); }
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> l[i];
  for (int i = 0; i < n; i++) cin >> r[i];
  med = 1;
  for (int i = 0; i < n - 1; i++) {
    num = min(r[i], r[i + 1]) - max(l[i], l[i + 1]) + 1ll;
    if (num <= 0)
      p[i] = 1;
    else
      p[i] = ((1ll -
               num * inv(((r[i] - l[i] + 1ll) * (r[i + 1] - l[i + 1] + 1ll)) %
                         mod)) %
                  mod +
              mod) %
             mod;
    med += p[i];
    var += (p[i] - (p[i] * p[i]) % mod) % mod;
    med %= mod;
    var %= mod;
  }
  for (int i = 0; i < n - 2; i++) {
    covar = 0;
    a = r[i] - l[i] + 1ll;
    b = r[i + 1] - l[i + 1] + 1ll;
    c = r[i + 2] - l[i + 2] + 1ll;
    tot = (a * ((b * c) % mod)) % mod;
    tmpl = max(l[i], l[i + 1]);
    tmpr = min(r[i], r[i + 1]);
    y = max(0ll, tmpr - tmpl + 1ll);
    tmpl = max(tmpl, l[i + 2]);
    tmpr = min(tmpr, r[i + 2]);
    x = max(0ll, tmpr - tmpl + 1ll);
    tmpl = max(l[i + 2], l[i + 1]);
    tmpr = min(r[i + 2], r[i + 1]);
    z = max(0ll, tmpr - tmpl + 1ll);
    covar += (x * (((-p[i]) * (-p[i + 1])) % mod)) % mod;
    covar %= mod;
    covar +=
        (((x * (c - 1ll)) % mod) * (((-p[i]) * (1ll - p[i + 1])) % mod)) % mod;
    covar %= mod;
    covar +=
        ((((y - x) * c) % mod) * (((-p[i]) * (1ll - p[i + 1])) % mod)) % mod;
    covar %= mod;
    covar +=
        (((x * (a - 1ll)) % mod) * (((1ll - p[i]) * (-p[i + 1])) % mod)) % mod;
    covar %= mod;
    covar +=
        ((((z - x) * a) % mod) * (((1ll - p[i]) * (-p[i + 1])) % mod)) % mod;
    covar %= mod;
    covar += (((tot - x - ((x * (c - 1ll)) % mod) - (((y - x) * c) % mod) -
                ((x * (a - 1ll)) % mod) - (((z - x) * a) % mod)) %
               mod) *
              (((1ll - p[i]) * (1ll - p[i + 1])) % mod)) %
             mod;
    covar *= inv(tot);
    covar %= mod;
    var += 2ll * covar;
    var %= mod;
  }
  var += mod;
  var %= mod;
  cout << (var + (med * med) % mod) % mod << "\n";
  return 0;
}
