#include <bits/stdc++.h>
const int MOD = (int)1e9 + 7;
inline int lgput(int a, int b) {
  int ans = 1;
  while (b > 0) {
    if (b & 1) ans = (1LL * ans * a) % MOD;
    b >>= 1;
    a = (1LL * a * a) % MOD;
  }
  return ans;
}
inline void mod(int &x) {
  if (x >= MOD) x -= MOD;
}
inline void add(int &x, int y) {
  x += y;
  mod(x);
}
inline void sub(int &x, int y) {
  x += MOD - y;
  mod(x);
}
inline void mul(int &x, int y) { x = (1LL * x * y) % MOD; }
inline int inv(int x) { return lgput(x, MOD - 2); }
using namespace std;
int main() {
  int i, n;
  ios::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  cin >> n;
  vector<int> l(n + 1), r(n + 1);
  for (i = 1; i <= n; i++) {
    cin >> l[i];
  }
  for (i = 1; i <= n; i++) {
    cin >> r[i];
    r[i]++;
  }
  vector<int> I(n + 1), E(n + 1);
  int sumI = 0;
  for (i = 1; i < n; i++) {
    int p = min(r[i], r[i + 1]) - max(l[i], l[i + 1]),
        q = 1LL * (r[i] - l[i]) * (r[i + 1] - l[i + 1]) % MOD;
    E[i] = 1LL * max(p, 0) * inv(q) % MOD;
    I[i] = (1 - E[i] + MOD) % MOD;
    add(sumI, I[i]);
  }
  int ans = sumI;
  mul(ans, ans);
  for (i = 1; i < n; i++) {
    sub(ans, 1LL * I[i] * I[i] % MOD);
    sub(ans, 2LL * I[i] * I[i - 1] % MOD);
    add(ans, I[i]);
    long long cur;
    if (i > 1) {
      cur = 1LL *
            (min(min(r[i], r[i + 1]), r[i - 1]) -
             max(max(l[i], l[i + 1]), l[i - 1])) *
            inv(1LL * (1LL * (r[i] - l[i]) * (r[i + 1] - l[i + 1]) % MOD) *
                (r[i - 1] - l[i - 1]) % MOD);
      cur = max(0LL, cur) % MOD;
      add(ans, 2 * (1 + cur) % MOD);
      sub(ans, 2LL * (E[i] + E[i - 1]) % MOD);
    }
  }
  add(ans, (1 + 2 * sumI) % MOD);
  cout << ans;
  return 0;
}
