#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e6 + 7;
const int P = 1e9 + 7;
int n, l[MAXN], r[MAXN];
long long fac[MAXN], ifac[MAXN], inv[MAXN], p[MAXN], q[MAXN];
long long sum, ans;
inline int add(int x, int y) {
  x += y;
  if (x >= P) x -= P;
  return x;
}
inline int max(int x, int y, int z) { return max(max(x, y), z); }
inline int min(int x, int y, int z) { return min(min(x, y), z); }
inline long long ksm(long long x, long long y) {
  long long ans = 1;
  while (y) {
    if (y & 1) ans = ans * x % P;
    x = x * x % P;
    y >>= 1;
  }
  return ans;
}
inline void init() {
  fac[0] = 1;
  for (int i = 1; i <= n; ++i) fac[i] = fac[i - 1] * i % P;
  ifac[n] = ksm(fac[n], P - 2);
  for (int i = n - 1; i >= 1; --i) ifac[i] = ifac[i + 1] * (i + 1) % P;
  ifac[0] = 1;
  inv[0] = 1;
  for (int i = 1; i <= n; ++i) inv[i] = 1ll * ifac[i] * fac[i - 1] % P;
}
inline long long I(int x) {
  return max(0ll, (min(r[x], r[x - 1]) - max(l[x], l[x - 1]) + 1) *
                      (ksm(r[x] - l[x] + 1, P - 2) *
                       ksm(r[x - 1] - l[x - 1] + 1, P - 2) % P) %
                      P);
}
inline long long I2(int x) {
  return (1 - q[x] - q[x + 1] +
          max(0ll, (min(r[x], r[x - 1], r[x + 1]) -
                    max(l[x], l[x + 1], l[x - 1]) + 1) *
                       (ksm(r[x] - l[x] + 1, P - 2) *
                        ksm(r[x - 1] - l[x - 1] + 1, P - 2) % P *
                        ksm(r[x + 1] - l[x + 1] + 1, P - 2) % P) %
                       P) +
          P + P) %
         P;
}
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]);
  p[1] = 1;
  q[1] = 0;
  sum = 1;
  for (int i = 2; i <= n; ++i) {
    q[i] = I(i);
    p[i] = (P + 1 - q[i]) % P;
    sum = add(sum, p[i]);
  }
  ans = sum;
  for (int i = 1; i <= n; ++i) {
    long long tmp = sum;
    for (int j = -1; j <= 1; ++j) tmp = add(tmp, P - p[i + j]);
    ans = add(ans, p[i] * tmp % P);
    if (i > 1) ans = add(ans, I2(i - 1));
    if (i < n) ans = add(ans, I2(i));
  }
  printf("%lld\n", ans);
  return 0;
}
