#include <bits/stdc++.h>
using namespace std;
using ii = pair<int, int>;
using ll = long long;
using vi = vector<int>;
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T>;
template <typename T>
ostream& operator<<(ostream& os, vector<T> v) {
  os << "[ ";
  for (auto e : v) os << e << " ";
  return os << "]";
}
template <typename T, typename V>
ostream& operator<<(ostream& os, set<T, V> v) {
  os << "{ ";
  for (auto e : v) os << e << " ";
  return os << "}";
}
template <typename T, typename V, typename S>
ostream& operator<<(ostream& os, map<T, V, S> v) {
  os << "{ ";
  for (auto e : v) os << e << " ";
  return os << "}";
}
template <typename T, typename V>
ostream& operator<<(ostream& os, pair<T, V> x) {
  return os << "( " << x.first << ", " << x.second << " )";
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (auto& e : v) is >> e;
  return is;
}
template <typename T, typename V>
istream& operator>>(istream& is, pair<T, V>& x) {
  return is >> x.first >> x.second;
}
void solve();
int main() { solve(); }
const int MOD = 1e9 + 7;
int mult(int a, int b) {
  int ans = 1LL * a * b % MOD;
  if (ans < 0) ans += MOD;
  return ans;
}
int add(int a, int b) {
  int ans = (a + b) % MOD;
  if (ans < 0) ans += MOD;
  return ans;
}
int powmod(int x, int e) {
  int ans = 1;
  while (e) {
    if (e & 1) {
      ans = mult(ans, x);
    }
    x = mult(x, x);
    e /= 2;
  }
  return ans;
}
int inv(int x) { return powmod(x, MOD - 2); }
int n, l[200005], r[200005];
int common(int i, int j) {
  return max(0, min(r[i], r[j]) - max(l[i], l[j]) + 1);
}
int common3(int i, int j, int k) {
  return max(0, min(r[i], min(r[j], r[k])) - max(l[i], max(l[j], l[k])) + 1);
}
void solve() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", l + i);
  for (int i = 1; i <= n; ++i) scanf("%d", r + i);
  int ans = 0;
  int sum = 0;
  int sum2 = 0;
  int sum3 = 0;
  int prevp = 0;
  for (int i = 1; i <= n; ++i) {
    int p;
    if (i == 1) {
      p = 1;
    } else {
      int c = common(i, i - 1);
      int s1 = r[i - 1] - l[i - 1] + 1;
      int s2 = r[i] - l[i] + 1;
      42;
      p = mult(mult(c, inv(s1)), mult(s2 - 1, inv(s2)));
      p = add(p, mult(s1 - c, inv(s1)));
      if (i == 2) {
        sum3 = add(sum3, mult(p, prevp));
      } else if (i > 2) {
        int A = 0, B = 0, C = 0;
        A = add(1, -prevp);
        B = add(1, -p);
        int c3 = common3(i - 2, i - 1, i);
        int s0 = r[i - 2] - l[i - 2] + 1;
        42;
        C = mult(common3(i - 2, i - 1, i),
                 mult(inv(s0), mult(inv(s1), inv(s2))));
        sum3 = add(sum3, -add(A, add(B, -C)));
        sum3 = add(sum3, 1);
        42;
      }
    }
    ans = add(ans, -mult(p, p));
    sum = add(sum, p);
    sum2 = add(sum2, mult(prevp, p));
    prevp = p;
  }
  ans = add(ans, mult(sum, sum));
  ans = add(ans, sum);
  ans = add(ans, -mult(2, sum2));
  ans = add(ans, mult(2, sum3));
  if (ans < 0) ans += MOD;
  printf("%d\n", ans);
}
