#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
using namespace std;
const int N = 200000 + 10;
const long long MOD = 1000000000 + 7;
const long long INF = 1000000010;
const long long LOG = 25;
int mul(int a, int b) { return (a * 1ll * b) % MOD; }
int add(int a, int b) {
  a += b;
  if (a >= MOD) a -= MOD;
  return a;
}
int minu(int a, int b) {
  a -= b;
  if (a < 0) a += MOD;
  return a;
}
int Uni(int l, int r, int l1, int r1) {
  l = max(l, l1);
  r = min(r, r1);
  return max(0, r - l + 1);
}
pair<int, int> Line(int l, int r, int l1, int r1) {
  return {max(l, l1), min(r, r1)};
}
int n, l[N], r[N], dp[N], pre[N], suf[N];
int POW(int x, int y) {
  int res = 1;
  while (y) {
    if (y & 1) res = mul(res, x);
    y >>= 1;
    x = mul(x, x);
  }
  return res;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> l[i];
  for (int i = 1; i <= n; i++) cin >> r[i];
  dp[0] = 0;
  pre[0] = 1;
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    pre[i] = mul(pre[i - 1], r[i] - l[i] + 1);
    if (i >= 2)
      dp[i] = add(mul(dp[i - 1], r[i] - l[i] + 1),
                  mul(pre[i - 2], Uni(l[i], r[i], l[i - 1], r[i - 1])));
  }
  suf[n + 1] = 1;
  for (int i = n; i >= 1; i--) suf[i] = mul(suf[i + 1], r[i] - l[i] + 1);
  for (int i = 2; i <= n; i++) {
    int x = r[i] - l[i] + 1;
    int y = Uni(l[i], r[i], l[i - 1], r[i - 1]);
    int res = dp[i - 1];
    res = minu(mul(i - 1, pre[i - 1]), dp[i - 1]);
    ans = add(ans, mul(res, mul(x - y, suf[i + 1])));
    if (i == 2) {
      int delta = r[i - 1] - l[i - 1];
      ans = add(ans, mul(delta, mul(y, suf[i + 1])));
      continue;
    }
    int z = Uni(l[i - 2], r[i - 2], Line(l[i - 1], r[i - 1], l[i], r[i]).first,
                Line(l[i - 1], r[i - 1], l[i], r[i]).second);
    if (z > 0) {
      int ted = r[i - 1] - l[i - 1] + 1;
      int Now = 0;
      Now = mul(dp[i - 2], ted - 1);
      int cnt = Uni(l[i - 2], r[i - 2], l[i - 1], r[i - 1]);
      Now = add(Now, mul(cnt - 1, pre[i - 3]));
      Now = minu(mul(mul(pre[i - 2], ted - 1), i - 1), Now);
      ans = add(ans, mul(Now, mul(z, suf[i + 1])));
    }
    if (y - z > 0) {
      int ted = r[i - 1] - l[i - 1] + 1;
      int Now = 0;
      Now = mul(dp[i - 2], ted - 1);
      int cnt = Uni(l[i - 2], r[i - 2], l[i - 1], r[i - 1]);
      Now = add(Now, mul(cnt, pre[i - 3]));
      Now = minu(mul(mul(pre[i - 2], ted - 1), i - 1), Now);
      ans = add(ans, mul(Now, mul(y - z, suf[i + 1])));
    }
  }
  ans = mul(2, ans);
  dp[n] = minu(mul(n, pre[n]), dp[n]);
  ans = add(ans, dp[n]);
  cout << mul(ans, POW(pre[n], MOD - 2));
  return 0;
}
