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
import java.util.Arrays;
import java.util.Scanner;

class Main {
	int n;
	int[] a;
	int[] b;
	final long MOD = 1_000_000_000 + 7;

	void run() {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		a = new int[n];
		b = new int[n];
		for (int i = 0; i < n; ++i) {
			a[i] = sc.nextInt();
		}
		for (int i = 0; i < n; ++i) {
			b[i] = sc.nextInt();
		}
		Arrays.sort(a);
		Arrays.sort(b);
		long[] c = new long[2 * n];
		for (int i = 0; i < n; ++i) {
			c[2 * i] = 2 * a[i];
			c[2 * i + 1] = 2 * b[i] + 1;
		}
		Arrays.sort(c);
		int out = 0, in = 0;
		long ans = 1;
		for (int i = 0; i < 2 * n; ++i) {
			if (c[i] % 2 == 1) {// outlet
				++out;
			} else {// pc
				++in;
			}
			while (out > 0 && in > 0) {
				ans = ans * Math.max(out, in) % MOD;
				--out;
				--in;
			}
		}
		if (out != 0 || in != 0)
			throw new AssertionError();
		System.out.println(ans);
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}

	public static void main(String[] args) {
		new Main().run();
	}
}