#include <bits/stdc++.h>
using namespace std;
template <typename T>
void read(T &x) {
  x = 0;
  char ch = getchar();
  long long f = 1;
  while (!isdigit(ch)) {
    if (ch == '-') f *= -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - 48;
    ch = getchar();
  }
  x *= f;
}
int mod = 1000000007;
inline int mul(int x, int y) { return 1ll * x * y % mod; }
int add(int x, int y) { return x + y >= mod ? x + y - mod : x + y; }
int sub(int x, int y) { return x - y < 0 ? x - y + mod : x - y; }
int sq(int x) { return 1ll * x * x % mod; }
int pow(int a, int b) {
  return b == 0 ? 1 : (b & 1 ? mul(a, sq(pow(a, b / 2))) : sq(pow(a, b / 2)));
}
const int N = 200020;
int n, l[N], r[N], cu[N];
int main() {
  int a = 0, b = 0;
  read(n);
  for (int i = 0; i < n; i++) read(l[i]);
  for (int i = 0; i < n; i++) read(r[i]);
  for (int i = 0; i < n - 1; i++) {
    int ml = max(l[i], l[i + 1]), mr = min(r[i], r[i + 1]);
    if (ml > mr)
      cu[i] = 1;
    else
      cu[i] = sub(
          1, mul(mr - ml + 1,
                 pow(mul(r[i] - l[i] + 1, r[i + 1] - l[i + 1] + 1), mod - 2)));
    a = add(a, cu[i]);
  }
  int csu = 0;
  for (int i = 1; i < n - 1; i++) {
    int cuu = 1;
    int ml3 = max(l[i - 1], max(l[i], l[i + 1])),
        mr3 = min(r[i - 1], min(r[i], r[i + 1]));
    int cho3 = pow(mul(r[i - 1] - l[i - 1] + 1,
                       mul(r[i + 1] - l[i + 1] + 1, r[i] - l[i] + 1)),
                   mod - 2);
    if (ml3 <= mr3) cuu = sub(cuu, mul(mr3 - ml3 + 1, cho3));
    int ml2 = max(l[i - 1], l[i]), mr2 = min(r[i - 1], r[i]);
    int isec = max(0, mr3 - ml3 + 1);
    if (ml2 <= mr2) {
      cuu = sub(cuu,
                mul(cho3, mul(mr2 - ml2 + 1 - isec, r[i + 1] - l[i + 1] + 1)));
      cuu = sub(cuu, mul(cho3, mul(isec, r[i + 1] - l[i + 1])));
    }
    ml2 = max(l[i + 1], l[i]), mr2 = min(r[i + 1], r[i]);
    if (ml2 <= mr2) {
      cuu = sub(cuu,
                mul(cho3, mul(mr2 - ml2 + 1 - isec, r[i - 1] - l[i - 1] + 1)));
      cuu = sub(cuu, mul(cho3, mul(isec, r[i - 1] - l[i - 1])));
    }
    b = add(b, mul(cu[i], csu));
    b = add(b, cuu);
    csu = add(csu, cu[i - 1]);
  }
  cout << add(1, add(mul(a, 3), mul(b, 2))) << endl;
  return 0;
}
