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.util.Arrays;
import java.util.Random;
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer; 

public class Number_of_permutations {
	public static long[] fact; 
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
	public static class store implements Comparable<store>{
		int a;
		int b;
		public store(int x,int y) {
			this.a=x;
			this.b=y;
		}
		public int compareTo(store s) {
			if(this.a==s.a) {
				return this.b-s.b;
			}
			return this.a-s.a;
		}
	}
	public static void fact_array(int n) {
		fact[1]=1;
        int mod=998244353;
        for(int i=2;i<=n;i++) {
        	fact[i]=((fact[i-1])%mod*i)%mod;
        }
	}
    public static long factorial(int n) {
    return fact[n];
    }
   static  void shuffleArray(int [] arr){
        int n = arr.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            int  tmp = arr[i];
            int randomPos = i + rnd.nextInt(n-i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }   
}
	public static void main(String[] args) {
		// TODO Auto-generated method stub
        FastReader s=new FastReader();
        int n=s.nextInt();
        int mod=998244353;
        fact=new long[n+1];
        fact_array(n);
        int[] arr1=new int[n];
        int[] arr2=new int[n];
        store[] input=new store[n];
        for(int i=0;i<n;i++) {
        	int a=s.nextInt();
        	int b=s.nextInt();
        	arr1[i]=a;
        	arr2[i]=b;
        	input[i]=new store(a, b);
        }
        shuffleArray(arr1);
        shuffleArray(arr1);
        Arrays.sort(arr1);
        Arrays.sort(arr2);
        long c1=1;
        for(int i=0;i<n;i++) {
        	int count=1;
        	while( (i+1)<n && arr1[i+1]==arr1[i]) {
        		i++;
        		count++;
        	}
        	c1=    (  (c1)%mod  * factorial(count) )%mod;
        }
        long c2=1;
        for(int i=0;i<n;i++) {
        	int count=1;
        	while( (i+1)<n && arr2[i+1]==arr2[i]) {
        		i++;
        		count++;
        	}
        	c2=    (  (c2)%mod  * factorial(count) )%mod;
        	//c2*=factorial(count);
        }
        Arrays.sort(input);
        boolean check=true;
        for(int i=0;i<n-1;i++) {
        	if(input[i].a>input[i+1].a || input[i].b>input[i+1].b   ) {
        		check=false;
        		break;
        	}
        }
        long c12=0;
        if(check==true) {
        	c12=1;
        	for(int i=0;i<n;i++) {
            	int count=1;
            	while( (i+1)<n && input[i].a==input[i+1].a && input[i].b==input[i+1].b   ) {
            		i++;
            		count++;
            	}
            	c12=    (  (c12)%mod  * factorial(count) )%mod;
            	//c12*=factorial(count);
            }
        }
        long f=fact[n];
        f=( f-c1       )%mod;
        if(f<0) {
        	f+=mod;
        }
        f=(f-c2)%mod;
        if(f<0) {
        	f+=mod;
        }
        f=(  (f)+(c12)        )%mod;
        if(f<0) {
        	f+=mod;
        }
        System.out.println(f);
	}

}
