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. 
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Random;
import java.util.StringTokenizer;
     
public class Solution{
    	
	static final int mod = 998244353;
    		
    	
    public static void main(String[] args) {
     
    	FastScanner fs = new FastScanner();
    	PrintWriter out = new PrintWriter(System.out);
    		
    		
    	int tt = 1;
    	while(tt-->0) {
    		
    		int n = fs.nextInt();
    		int[][] a = new int[n][2];
    		
    		int[][] cnt = new int[n+1][2];
    		
    		
    		for(int i=0;i<n;i++) {
    			a[i][0] = fs.nextInt();
    			a[i][1] = fs.nextInt();
    			cnt[a[i][0]][0]++; cnt[a[i][1]][1]++;
    		}
    		
    		
    		int[] fact = new int[n+1];
    		fact[0] = 1;
    		for(int i=1;i<=n;i++)
    			fact[i] = mul(fact[i-1], i);
    		
    		
    		int num1 = 1; int num2 = 1;
    		
    		for(int i=1;i<=n;i++) {
    			num1 = mul(num1, fact[cnt[i][0]]);
    			num2 = mul(num2, fact[cnt[i][1]]);
    		}
    		
    		Arrays.sort(a, (x,y) -> (x[0]==y[0])?(x[1]-y[1]):(x[0]-y[0]));
    		
    		int num3 = 1;
    		
    		boolean bool = true;
    		for(int i=0;i<n;i++) {
    			int j = i;
    			while(i<n-1 && a[i+1][0]==a[j][0] && a[i+1][1]==a[j][1]) i++;
    			num3 = mul(num3, fact[i-j+1]);
    			if(i<n-1 && a[i+1][1]<a[i][1]) { 
    				bool = false;
    				break;
    			}
    		}
    		
    		if(!bool) num3 = 0;
    		
    		
    		
    		long ans = ((long)fact[n] - num1 - num2 + num3 + 2*mod)%mod;
    		
    		
    		out.println(ans);
    		
    		
    	}
    		
    	out.close();
    		
    }
    
    
    
  
    	
    	
    
    static int sum(int a, int b) {
    	return (a+b)%mod;
    }
    
    
    
    
    
    static int mul(int a, int b) {
    	return (int)(((long)a*b)%mod);
    }
    
    	
    	
    	
    	
    	
    	
    static final Random random=new Random();
    	
    static void ruffleSort(int[] a) {
    	int n=a.length;//shuffle, then sort 
    	for (int i=0; i<n; i++) {
    		int oi=random.nextInt(n); int temp=a[oi];
    		a[oi]=a[i]; a[i]=temp;
    	}
    	Arrays.sort(a);
    }
    	
    	
    	
    static class FastScanner{
    	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    	StringTokenizer st = new StringTokenizer("");
     
    	public String next(){
    		while(!st.hasMoreElements()){
    			try{
    				st = new StringTokenizer(br.readLine());
    			} catch(IOException e){
    				e.printStackTrace();
    			}
    		}
    		return st.nextToken();
    	}
    		
    	public String nextLine() throws IOException {
    		return br.readLine();
    	}
    		
    	public int nextInt(){
    		return Integer.parseInt(next());
    	}
     
    	public int[] readArray(int n){
    		int[] a = new int[n];
    		for(int i=0;i<n;i++)
    			a[i] = nextInt();
    		return a;
    	}
    		
    	public long nextLong() {
    		return Long.parseLong(next());
    	}
    		
    	public char nextChar() {
    		return next().toCharArray()[0];
    	}
    }
   	
}