You are given a sequence of n pairs of integers: (a_1, b_1), (a_2, b_2), ... , (a_n, b_n). This sequence is called bad if it is sorted in non-descending order by first elements or if it is sorted in non-descending order by second elements. Otherwise the sequence is good. There are examples of good and bad sequences:

  * s = [(1, 2), (3, 2), (3, 1)] is bad because the sequence of first elements is sorted: [1, 3, 3]; 
  * s = [(1, 2), (3, 2), (1, 2)] is bad because the sequence of second elements is sorted: [2, 2, 2]; 
  * s = [(1, 1), (2, 2), (3, 3)] is bad because both sequences (the sequence of first elements and the sequence of second elements) are sorted; 
  * s = [(1, 3), (3, 3), (2, 2)] is good because neither the sequence of first elements ([1, 3, 2]) nor the sequence of second elements ([3, 3, 2]) is sorted. 



Calculate the number of permutations of size n such that after applying this permutation to the sequence s it turns into a good sequence. 

A permutation p of size n is a sequence p_1, p_2, ... , p_n consisting of n distinct integers from 1 to n (1 ≤ p_i ≤ n). If you apply permutation p_1, p_2, ... , p_n to the sequence s_1, s_2, ... , s_n you get the sequence s_{p_1}, s_{p_2}, ... , s_{p_n}. For example, if s = [(1, 2), (1, 3), (2, 3)] and p = [2, 3, 1] then s turns into [(1, 3), (2, 3), (1, 2)].

Input

The first line contains one integer n (1 ≤ n ≤ 3 ⋅ 10^5).

The next n lines contains description of sequence s. The i-th line contains two integers a_i and b_i (1 ≤ a_i, b_i ≤ n) — the first and second elements of i-th pair in the sequence.

The sequence s may contain equal elements.

Output

Print the number of permutations of size n such that after applying this permutation to the sequence s it turns into a good sequence. Print the answer modulo 998244353 (a prime number).

Examples

Input


3
1 1
2 2
3 1


Output


3


Input


4
2 3
2 2
2 1
2 4


Output


0


Input


3
1 1
1 1
2 3


Output


4

Note

In first test case there are six permutations of size 3: 

  1. if p = [1, 2, 3], then s = [(1, 1), (2, 2), (3, 1)] — bad sequence (sorted by first elements); 
  2. if p = [1, 3, 2], then s = [(1, 1), (3, 1), (2, 2)] — bad sequence (sorted by second elements); 
  3. if p = [2, 1, 3], then s = [(2, 2), (1, 1), (3, 1)] — good sequence; 
  4. if p = [2, 3, 1], then s = [(2, 2), (3, 1), (1, 1)] — good sequence; 
  5. if p = [3, 1, 2], then s = [(3, 1), (1, 1), (2, 2)] — bad sequence (sorted by second elements); 
  6. if p = [3, 2, 1], then s = [(3, 1), (2, 2), (1, 1)] — good sequence. 
// https://codeforces.com/contest/1207/submission/59312240 (rainboy)
import java.io.*;
import java.util.*;

public class CF1207D extends PrintWriter {
	CF1207D() { super(System.out, true); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1207D o = new CF1207D(); o.main(); o.flush();
	}

	static final int MD = 998244353;
	void main() {
		int n = sc.nextInt();
		int[] ff = new int[n + 1];
		long f = 1;
		for (int i = 0; i <= n; i++) {
			ff[i] = (int) f;
			f = f * (i + 1) % MD;
		}
		int[] aa = new int[n];
		int[] bb = new int[n];
		Integer[] ii = new Integer[n];
		for (int i = 0; i < n; i++) {
			aa[i] = sc.nextInt();
			bb[i] = sc.nextInt();
			ii[i] = i;
		}
		Arrays.sort(ii, (i, j) -> aa[i] != aa[j] ? aa[i] - aa[j] : bb[i] - bb[j]);
		boolean sorted = true;
		for (int i = 1; i < n; i++)
			if (!(aa[ii[i - 1]] <= aa[ii[i]] && bb[ii[i - 1]] <= bb[ii[i]])) {
				sorted = false;
				break;
			}
		long r = 0;
		if (sorted) {
			r = 1;
			for (int i = 0, j; i < n; i = j) {
				j = i + 1;
				while (j < n && aa[ii[j]] == aa[ii[i]] && bb[ii[j]] == bb[ii[i]])
					j++;
				r = r * ff[j - i] % MD;
			}
		}
		long p = 1;
		for (int i = 0, j; i < n; i = j) {
			j = i + 1;
			while (j < n && aa[ii[j]] == aa[ii[i]])
				j++;
			p = p * ff[j - i] % MD;
		}
		Arrays.sort(ii, (i, j) -> bb[i] - bb[j]);
		long q = 1;
		for (int i = 0, j; i < n; i = j) {
			j = i + 1;
			while (j < n && bb[ii[j]] == bb[ii[i]])
				j++;
			q = q * ff[j - i] % MD;
		}
		println(((ff[n] - p - q + r) % MD + MD) % MD);
	}
}
