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 = long long;
using P = pair<int, int>;

const ll MOD = 1000000007;

ll modpow(ll x, ll n, ll mod = MOD) {
    ll res = 1;
    while (n > 0) {
        if (n & 1) res = res * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return res;
}

ll f[100005];

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vector<int> a(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    sort(a.begin(), a.end());

    vector<int> b(n);
    for (int i = 0; i < n; i++) {
        cin >> b[i];
    }
    sort(b.begin(), b.end());

    f[0] = 1;
    for (int i = 1; i <= n; i++) {
        f[i] = f[i-1]*i%MOD;
    }

    ll ans = 1;
    for (int i = 0, j = 1; i < n; i++) {
        int L1 = min(a[i], b[i]);
        int R1 = max(a[i], b[i]);
        while (j < n) {
            int L2 = min(a[j], b[j]);
            int R2 = max(a[j], b[j]);
            if (R1 < L2) break;
            j++;
        }

        int num = max(j - i, 0);
        (ans *= num) %= MOD;
    }
    cout << ans << endl;
    return 0;
}