#include <bits/stdc++.h>
const int N = 200005;
const int cIz = 1000000007;
inline int Pow(int a, int b) {
  int ans = 1;
  for (; b; b >>= 1) {
    if (b & 1) ans = (long long)ans * a % cIz;
    a = (long long)a * a % cIz;
  }
  return ans;
}
inline int Inv(int a) { return Pow(a, cIz - 2); }
template <typename T>
inline void add(int &a, T b) {
  a = (a + b) % cIz;
}
int n, l[N], r[N], inv_len[N];
inline int len(int i) { return r[i] - l[i] + 1; }
void get_inv() {
  static int mul[N];
  mul[0] = 1;
  for (int i = 1; i <= n; ++i) {
    mul[i] = (long long)mul[i - 1] * len(i) % cIz;
  }
  int tmp = Inv(mul[n]);
  for (int i = n; i; --i) {
    inv_len[i] = (long long)tmp * mul[i - 1] % cIz;
    tmp = (long long)tmp * len(i) % cIz;
  }
}
inline int calc(int x, int p = 1) {
  int L = l[x], R = r[x], div = inv_len[x];
  while (p--) {
    --x;
    L = std::max(L, l[x]);
    R = std::min(R, r[x]);
    div = (long long)div * inv_len[x] % cIz;
  }
  return L <= R ? (R - L + 1ll) * div % cIz : 0;
}
int f[N], sumf[N];
int main() {
  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);
  get_inv();
  int ans = 1;
  for (int i = 2; i <= n; ++i) {
    f[i] = 1 - calc(i);
    add(sumf[i] = sumf[i - 1], f[i]);
    add(ans, 3ll * f[i]);
    add(ans, 2ll * f[i] * sumf[i - 2]);
    if (i > 2) add(ans, 2 * (f[i - 1] + f[i] - 1ll + calc(i, 2)));
  }
  add(ans, cIz);
  printf("%d\n", ans);
  return 0;
}
