There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.

Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.

In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.

Constraints

* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.

Input

The input is given from Standard Input in the following format:


N
a_1
:
a_N
b_1
:
b_N


Output

Print the number of ways to minimize the total length of the cables, modulo 10^9+7.

Examples

Input

2
0
10
20
30


Output

2


Input

3
3
10
8
7
12
5


Output

1
#include <bits/stdc++.h>

using ll = long long;
using ld = long double;
constexpr ll inf = static_cast<ll>(1e17);
constexpr int iinf = static_cast<int>(1e9);
constexpr ll mod = static_cast<ll>(1e9 + 7);

int n;
std::pair<ll, ll> ab[200005];
int main()
{
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    std::cin >> n;

    for (int i = 0; i < 2 * n; ++i) {
        ll a;
        std::cin >> a;

        ab[i] = { a,(i < n ? 1 : -1) };
    }

    std::sort(ab, ab + 2 * n);

    ll ans = 1, sum = 0;
    for (int i = 0; i < 2 * n; ++i) {
        auto s = ab[i].second;
        if (sum == 0 || s * sum > 0) {
            sum += s;
        }
        else {
            ans = ans * std::abs(sum) % mod;
            sum += s;
        }
    }

    std::cout << ans << std::endl;

    return 0;
}
