#include <bits/stdc++.h>
using namespace std;
template <typename T>
bool cmax(T &a, T b) {
  return (a < b) ? a = b, 1 : 0;
}
template <typename T>
bool cmin(T &a, T b) {
  return (a > b) ? a = b, 1 : 0;
}
template <typename T>
T read() {
  T ans = 0, f = 1;
  char ch = getchar();
  while (!isdigit(ch) && ch != '-') ch = getchar();
  if (ch == '-') f = -1, ch = getchar();
  while (isdigit(ch))
    ans = (ans << 3) + (ans << 1) + (ch - '0'), ch = getchar();
  return ans * f;
}
template <typename T>
void write(T x, char y) {
  if (x == 0) {
    putchar('0'), putchar(y);
    return;
  }
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  static char wr[20];
  int top = 0;
  for (; x; x /= 10) wr[++top] = x % 10 + '0';
  while (top) putchar(wr[top--]);
  putchar(y);
}
void file() {}
const int N = 2e5 + 5;
const int mo = 1e9 + 7;
int n, l[N], r[N];
void input() {
  n = read<int>();
  for (register int i = (int)(1); i <= (int)(n); ++i) l[i] = read<int>();
  for (register int i = (int)(1); i <= (int)(n); ++i) r[i] = read<int>();
}
int power(int x, int y) {
  int res = 1;
  for (; y; x = 1ll * x * x % mo, y >>= 1)
    if (y & 1) res = 1ll * res * x % mo;
  return res;
}
int p[N], pre[N], suf[N], q[N];
int cal(int x, int y, int z) {
  return 1ll *
         (max(0, min(min(r[x], r[y]), r[z]) - max(max(l[x], l[y]), l[z]) + 1)) *
         power(1ll * (r[x] - l[x] + 1) * (r[y] - l[y] + 1) % mo *
                   (r[z] - l[z] + 1) % mo,
               mo - 2) %
         mo;
}
void work() {
  int ans = 0;
  for (register int i = (int)(1); i <= (int)(n); ++i) {
    p[i] = 1ll * max(0, min(r[i], r[i - 1]) - max(l[i], l[i - 1]) + 1) *
           power(1ll * (r[i] - l[i] + 1) * (r[i - 1] - l[i - 1] + 1) % mo,
                 mo - 2) %
           mo;
    q[i] = (1 - p[i] + mo) % mo;
  }
  for (register int i = (int)(1); i <= (int)(n); ++i)
    pre[i] = (pre[i - 1] + q[i]) % mo;
  for (register int i = (int)(n); i >= (int)(1); --i)
    suf[i] = (suf[i + 1] + q[i]) % mo;
  for (register int i = (int)(1); i <= (int)(n); ++i) {
    int res;
    if (i == 1)
      res = 1ll * q[i] * suf[i + 2] % mo;
    else if (i == n)
      res = 1ll * q[i] * pre[i - 2] % mo;
    else
      res = 1ll * q[i] * (pre[i - 2] + suf[i + 2]) % mo;
    if (1 < i)
      res =
          (res + (1ll - p[i] - p[i - 1] + cal(i - 2, i - 1, i)) % mo + mo) % mo;
    if (i < n)
      res =
          (res + (1ll - p[i] - p[i + 1] + cal(i - 1, i, i + 1)) % mo + mo) % mo;
    res = (res + q[i]) % mo;
    ans = (ans + res) % mo;
  }
  printf("%d\n", (ans + mo) % mo);
}
int main() {
  file();
  input();
  work();
  return 0;
}
