#include <bits/stdc++.h>
using namespace std;
const int MOD = int(1e9) + 7;
int norm(int a) {
  while (a >= MOD) a -= MOD;
  while (a < 0) a += MOD;
  return a;
}
int mul(int a, int b) { return int(a * 1ll * b % MOD); }
int binPow(int a, int k) {
  int ans = 1;
  for (; k > 0; k >>= 1) {
    if (k & 1) ans = mul(ans, a);
    a = mul(a, a);
  }
  return ans;
}
int inv(int a) {
  int b = binPow(a, MOD - 2);
  assert(mul(a, b) == 1);
  return b;
}
int n;
vector<int> l, r;
inline bool read() {
  if (!(cin >> n)) return false;
  l.resize(n);
  r.resize(n);
  for (int i = int(0); i < int(n); i++) cin >> l[i];
  for (int i = int(0); i < int(n); i++) {
    cin >> r[i];
    r[i]++;
  }
  return true;
}
vector<int> p;
int calcEq(int i0) {
  int i1 = i0 + 1;
  int pSame = 0;
  if (i0 > 0) {
    int cnt =
        max(0, min({r[i0 - 1], r[i0], r[i1]}) - max({l[i0 - 1], l[i0], l[i1]}));
    pSame =
        mul(cnt,
            inv(mul(mul(r[i0 - 1] - l[i0 - 1], r[i0] - l[i0]), r[i1] - l[i1])));
  }
  return norm(1 - norm(2 - p[i0] - p[i1]) + pSame);
}
inline void solve() {
  p.assign(n, 0);
  p[0] = 1;
  for (int i = int(1); i < int(n); i++) {
    int cnt = max(0, min(r[i - 1], r[i]) - max(l[i - 1], l[i]));
    p[i] = norm(1 - mul(cnt, inv(mul(r[i - 1] - l[i - 1], r[i] - l[i]))));
  }
  int sum = 0;
  for (int i = int(0); i < int(n); i++) sum = norm(sum + p[i]);
  int ans = 0;
  for (int i = int(0); i < int(n); i++) {
    int curS = sum;
    for (int j = max(0, i - 1); j < min(n, i + 2); j++)
      curS = norm(curS - p[j]);
    ans = norm(ans + mul(p[i], curS));
    if (i > 0) ans = norm(ans + calcEq(i - 1));
    ans = norm(ans + p[i]);
    if (i + 1 < n) ans = norm(ans + calcEq(i));
  }
  cout << ans << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  cout << fixed << setprecision(15);
  if (read()) {
    solve();
  }
  return 0;
}
