#include <bits/stdc++.h>
template <typename Tp>
void read(Tp &x) {
  x = 0;
  int op = 1;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') op = -1;
    c = getchar();
  }
  while (isdigit(c)) {
    x = (x << 1) + (x << 3) + c - '0';
    c = getchar();
  }
  x *= op;
}
int max(int a, int b) { return a > b ? a : b; }
int min(int a, int b) { return a < b ? a : b; }
const int MN = 200000 + 10;
const int Mod = 1e9 + 7;
int Pls(int x, int y) {
  x += y;
  if (x >= Mod) x -= Mod;
  return x;
}
int Sub(int x, int y) {
  x -= y;
  if (x < 0) x += Mod;
  return x;
}
int power(int x, int p) {
  int ret = 1;
  while (p) {
    if (p & 1) ret = 1ll * ret * x % Mod;
    x = 1ll * x * x % Mod;
    p >>= 1;
  }
  return ret;
}
int Inv(int x) { return power(x, Mod - 2); }
struct sec {
  int l, r;
  sec() { l = r = 0; }
  sec(int _l, int _r) : l(_l), r(_r) {}
};
sec cross(sec x, sec y) {
  int l = max(x.l, y.l), r = min(x.r, y.r);
  if (l > r)
    return sec(1, 0);
  else
    return sec(l, r);
}
int len(sec x) { return x.r - x.l + 1; }
int N;
sec r[MN], s[MN];
int P[MN];
int E1, E2;
int main() {
  read(N);
  for (int i = 1; i <= N; ++i) read(r[i].l);
  for (int i = 1; i <= N; ++i) read(r[i].r);
  P[1] = 1;
  E1 = 1;
  for (int i = 2; i <= N; ++i) {
    s[i] = cross(r[i], r[i - 1]);
    P[i] = 1ll * len(s[i]) * Inv(1ll * len(r[i]) * len(r[i - 1]) % Mod) % Mod;
    P[i] = Sub(1, P[i]);
    E1 = Pls(E1, P[i]);
  }
  E2 = P[2];
  int sum = P[1];
  for (int i = 3; i <= N; ++i) {
    E2 = Pls(E2, 1ll * sum * P[i] % Mod);
    int res = 0;
    sec cur = cross(s[i - 1], r[i]);
    res = Pls(res, len(cur));
    res = Pls(res, Pls(1ll * len(cur) * (len(r[i]) - 1) % Mod,
                       1ll * (len(s[i - 1]) - len(cur)) * len(r[i]) % Mod));
    res = Pls(res, Pls(1ll * len(cur) * (len(r[i - 2]) - 1) % Mod,
                       1ll * (len(s[i]) - len(cur)) * len(r[i - 2]) % Mod));
    res = Sub(1, 1ll * res *
                     Inv(1ll * len(r[i]) * len(r[i - 1]) % Mod * len(r[i - 2]) %
                         Mod) %
                     Mod);
    E2 = Pls(E2, res);
    sum = Pls(sum, P[i - 1]);
  }
  E2 = (2ll * E2 + E1) % Mod;
  printf("%d", E2);
  return 0;
}
