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 namespace std;
using ll = int64_t;
using P = pair<ll, ll>;

const ll INF = 5e15;
const ll MOD = 1e9 + 7;

vector<P> V;
ll cnt1 = 0, cnt2 = 0;

void update(ll idx) {
    if (V[idx].second == 0) cnt1++;
    if (V[idx].second == 1) cnt2++;
}

int main() {
    ll ans = 1;
    ll N;
    cin >> N;
    for (ll i = 0; i < N; i++) {
        ll a;
        cin >> a;
        V.push_back(P(a, 0));
    }
    for (ll i = 0; i < N; i++) {
        ll b;
        cin >> b;
        V.push_back(P(b, 1));
    }
    sort(V.begin(), V.end());
    for (ll i = 0; i < 2 * N; i++) {
        update(i);
        if (cnt1 && cnt2) {
            ans *= max(cnt1, cnt2);
            ans %= MOD;
            cnt1--;
            cnt2--;
        }
    }
    cout << ans << endl;
    return 0;
}
