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.ArrayDeque;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner stdin = new Scanner(System.in);

        int n = Integer.parseInt(stdin.nextLine());
        List<Point> points = new ArrayList<>();
        for (int i = 0; i < n; i++) points.add(new Point(Integer.parseInt(stdin.nextLine()), true));
        for (int i = 0; i < n; i++) points.add(new Point(Integer.parseInt(stdin.nextLine()), false));
        Collections.sort(points, Comparator.comparing(point -> point.x));

        long ans = 1;
        long mod = 1_000_000_000 + 7;
        Deque<Point> pcs = new ArrayDeque<>();
        Deque<Point> powers = new ArrayDeque<>();
        for (Point point : points) {
            if (point.pc) {
                if (powers.isEmpty()) {
                    pcs.addLast(point);
                } else {
                    ans = (ans * powers.size()) % mod;
                    powers.pollLast();

                }
            } else {
                if (pcs.isEmpty()) {
                    powers.addLast(point);
                } else {
                    ans = (ans * pcs.size()) % mod;
                    pcs.pollLast();
                }
            }
        }

        System.out.println(ans);
    }

    private static class Point {
        private int x;
        private boolean pc;

        public Point(int x, boolean pc) {
            super();
            this.x = x;
            this.pc = pc;
        }
    }
}
