#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 7;
const int inf = 0x3f3f3f3f;
const long long INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-10;
const double PI = acos(-1);
template <class T, class S>
inline void add(T &a, S b) {
  a += b;
  if (a >= mod) a -= mod;
}
template <class T, class S>
inline void sub(T &a, S b) {
  a -= b;
  if (a < 0) a += mod;
}
template <class T, class S>
inline bool chkmax(T &a, S b) {
  return a < b ? a = b, true : false;
}
template <class T, class S>
inline bool chkmin(T &a, S b) {
  return a > b ? a = b, true : false;
}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int power(int a, int b) {
  int ans = 1;
  while (b) {
    if (b & 1) ans = 1LL * ans * a % mod;
    a = 1LL * a * a % mod;
    b >>= 1;
  }
  return ans;
}
int n, l[N], r[N];
int p[N], q[N];
int pre[N];
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &l[i]);
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d", &r[i]);
    r[i]++;
  }
  q[1] = 0;
  p[1] = 1;
  for (int i = 1; i <= n; i++) {
    int L = max(l[i], l[i - 1]);
    int R = min(r[i], r[i - 1]);
    if (R > L) {
      q[i] = 1LL * (R - L) * power(r[i] - l[i], mod - 2) % mod *
             power(r[i - 1] - l[i - 1], mod - 2) % mod;
    }
    p[i] = (1 - q[i] + mod) % mod;
  }
  for (int i = 1; i <= n; i++) {
    pre[i] = (pre[i - 1] + p[i]) % mod;
  }
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    add(ans, p[i]);
  }
  for (int i = 1; i <= n; i++) {
    if (i - 2 >= 1) {
      add(ans, 2LL * p[i] * pre[i - 2] % mod);
    }
  }
  r[0] = -inf;
  l[0] = inf;
  for (int i = 1; i < n; i++) {
    int ret = ((1 - q[i] - q[i + 1]) % mod + mod) % mod;
    int R = min(r[i - 1], min(r[i], r[i + 1]));
    int L = max(l[i - 1], max(l[i], l[i + 1]));
    int tmp = 0;
    if (R > L) {
      tmp = R - L;
      tmp = 1LL * tmp * power(r[i - 1] - l[i - 1], mod - 2) % mod;
      tmp = 1LL * tmp * power(r[i] - l[i], mod - 2) % mod;
      tmp = 1LL * tmp * power(r[i + 1] - l[i + 1], mod - 2) % mod;
    }
    add(ret, tmp);
    add(ans, 2LL * ret % mod);
  }
  printf("%d\n", ans);
  return 0;
}
