#include <bits/stdc++.h>
using namespace std;
void Freopen() {
  freopen(
      "title"
      ".in",
      "r", stdin);
  freopen(
      "title"
      ".out",
      "w", stdout);
}
int read() {
  int g = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || '9' < ch) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while ('0' <= ch && ch <= '9') {
    g = g * 10 + ch - '0';
    ch = getchar();
  }
  return g * f;
}
const int N = 2e5 + 5;
const int mod = 1e9 + 7;
int pre[N], suf[N], L[N], R[N], len[N], n, p[N], q[N];
int ksm(int x, int y) {
  int re = 1;
  for (; y; y >>= 1, x = 1ll * x * x % mod)
    if (y & 1) re = 1ll * re * x % mod;
  return re;
}
int calc(int x) {
  int re = 0;
  if (x - 2 > 0) re = (re + pre[x - 2]) % mod;
  if (x + 2 <= n) re = (re + suf[x + 2]) % mod;
  return re;
}
int solve(int x, int y, int z) {
  return max(
      0ll, 1ll * (min(R[x], min(R[y], R[z])) - max(L[x], max(L[y], L[z])) + 1) *
               ksm(1ll * len[x] * len[y] % mod * len[z] % mod, mod - 2) % mod);
}
signed main() {
  n = read();
  for (int i = (1); i <= (n); i++) L[i] = read();
  for (int i = (1); i <= (n); i++) R[i] = read();
  for (int i = (1); i <= (n); i++) len[i] = R[i] - L[i] + 1;
  q[1] = 0;
  for (int i = (2); i <= (n); i++)
    q[i] = max(0ll, 1ll * (min(R[i], R[i - 1]) - max(L[i], L[i - 1]) + 1) *
                        ksm(1ll * len[i] * len[i - 1] % mod, mod - 2) % mod);
  for (int i = (1); i <= (n); i++) p[i] = (1 + mod - q[i]) % mod;
  int ans = 0;
  for (int i = (1); i <= (n); i++) ans = (ans + p[i]) % mod;
  for (int i = (1); i <= (n); i++) pre[i] = (pre[i - 1] + p[i]) % mod;
  for (int i = (n); i >= (1); i--) suf[i] = (suf[i + 1] + p[i]) % mod;
  for (int i = (1); i <= (n); i++)
    ans = (ans + 1ll * p[i] * calc(i) % mod) % mod;
  for (int i = (1); i <= (n - 2); i++) {
    int res =
        (1ll - q[i + 1] + mod - q[i + 2] + mod + solve(i, i + 1, i + 2)) % mod;
    ans = (ans + 2ll * res % mod) % mod;
  }
  ans = (ans + 2ll * p[2] % mod) % mod;
  return cout << ans, signed();
}
