#include <bits/stdc++.h>
using namespace std;
void read(int &x) {
  x = 0;
  int f = 1;
  char ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') f = -f;
  for (; isdigit(ch); ch = getchar()) x = x * 10 + ch - '0';
  x *= f;
}
void print(int x) {
  if (x < 0) putchar('-'), x = -x;
  if (!x) return;
  print(x / 10), putchar(x % 10 + 48);
}
void write(int x) {
  if (!x)
    putchar('0');
  else
    print(x);
  putchar('\n');
}
const int maxn = 1e6 + 10;
const int inf = 1e9;
const double eps = 1e-8;
const int mod = 1e9 + 7;
int n, l[maxn], r[maxn], ans, p[maxn];
int qpow(int a, int x) {
  int res = 1;
  for (; x; x >>= 1, a = 1ll * a * a % mod)
    if (x & 1) res = 1ll * res * a % mod;
  return res;
}
int calc(int x) {
  if (!x || x >= n) return 0;
  int a = max(max(l[x], l[x - 1]), l[x + 1]);
  int b = min(min(r[x], r[x - 1]), r[x + 1]);
  int all = 1ll * (r[x] - l[x] + 1) * (r[x - 1] - l[x - 1] + 1) % mod *
            (r[x + 1] - l[x + 1] + 1) % mod;
  int res = (all + max(0, b - a + 1)) % mod;
  res = (res - 1ll * max(0, (min(r[x], r[x - 1]) - max(l[x], l[x - 1]) + 1)) *
                   (r[x + 1] - l[x + 1] + 1) % mod) %
        mod;
  res = (res - 1ll * max(0, (min(r[x], r[x + 1]) - max(l[x], l[x + 1]) + 1)) *
                   (r[x - 1] - l[x - 1] + 1) % mod) %
        mod;
  res = 1ll * res * qpow(all, mod - 2) % mod;
  return res;
}
int main() {
  read(n);
  for (int i = 1; i <= n; i++) read(l[i]);
  int sum = 0;
  for (int i = 1; i <= n; i++) read(r[i]);
  for (int i = 1; i <= n; i++) {
    p[i] = max(0, min(r[i], r[i - 1]) - max(l[i], l[i - 1]) + 1);
    p[i] = 1ll * p[i] *
           qpow(1ll * (r[i] - l[i] + 1) * (r[i - 1] - l[i - 1] + 1) % mod,
                mod - 2) %
           mod;
    p[i] = (1 - p[i] + mod) % mod;
    sum = (sum + p[i]) % mod;
  }
  for (int i = 1; i <= n; i++) {
    ans = (ans +
           1ll * p[i] * (1ll * sum - p[i] - p[i - 1] - p[i + 1] + 1) % mod) %
          mod;
    ans = (ans + calc(i - 1)) % mod;
    ans = (ans + calc(i)) % mod;
  }
  write((ans + mod) % mod);
  return 0;
}
