#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
const long long mod = 1e9 + 7;
long long L[N], R[N], Len[N];
long long p[N];
long long fp(long long a, long long p) {
  long long r = 1;
  while (p) {
    if (p & 1) r = (r * a) % mod;
    a = (a * a) % mod;
    p >>= 1;
  }
  return r;
}
long long Inv(long long x) {
  x %= mod;
  return fp(x, mod - 2);
}
long long add(long long x, long long y) {
  x %= mod;
  y %= mod;
  return (x + y) % mod;
}
long long sub(long long x, long long y) {
  x %= mod;
  y %= mod;
  return (x - y + mod) % mod;
}
long long mul(long long x, long long y) {
  x %= mod;
  y %= mod;
  return (x * y) % mod;
}
pair<long long, long long> Intersect(long long l1, long long r1, long long l2,
                                     long long r2) {
  if (r1 < l2 || r2 < l1) return make_pair(0, -1);
  return make_pair(max(l1, l2), min(r1, r2));
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%I64d", &L[i]);
  for (int i = 1; i <= n; i++) scanf("%I64d", &R[i]);
  L[0] = L[0] = -1;
  for (int i = 1; i <= n; i++) {
    pair<long long, long long> Int = Intersect(L[i], R[i], L[i - 1], R[i - 1]);
    Len[i] = Int.second - Int.first + 1;
    p[i] = mul(sub((R[i] - L[i] + 1) * (R[i - 1] - L[i - 1] + 1), Len[i]),
               Inv((R[i] - L[i] + 1) * (R[i - 1] - L[i - 1] + 1)));
  }
  long long sum = 0, ans = 0;
  for (int i = 1; i <= n; i++) {
    ans = add(ans, p[i]);
    if (i > 2) {
      sum = add(sum, p[i - 2]);
      ans = add(ans, mul(2, mul(p[i], sum)));
    }
  }
  for (int i = 2; i <= n; i++) {
    pair<long long, long long> Int =
        Intersect(L[i - 2], R[i - 2], L[i - 1], R[i - 1]);
    Int = Intersect(Int.first, Int.second, L[i], R[i]);
    long long LEN = Int.second - Int.first + 1;
    long long p123 = sub(add(mul((R[i] - L[i] + 1), Len[i - 1]),
                             mul((R[i - 2] - L[i - 2] + 1), Len[i])),
                         LEN);
    long long P = sub((((R[i] - L[i] + 1) * (R[i - 1] - L[i - 1] + 1)) % mod) *
                          (R[i - 2] - L[i - 2] + 1),
                      p123);
    P = mul(P, Inv((((R[i] - L[i] + 1) * (R[i - 1] - L[i - 1] + 1)) % mod) *
                   (R[i - 2] - L[i - 2] + 1)));
    ans = add(ans, mul(2, P));
  }
  printf("%I64d\n", ans);
  return 0;
}
