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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader sc = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, sc, out);
        out.close();
    }

    static class Task {
    	public static final long Mod=998244353;
    	
        public void solve(int testNumber, InputReader sc, PrintWriter out) {
            int n=sc.nextInt();
            long[] fac=new long[n+1];
            fac[0]=1;
            for(int i=1;i<=n;i++)
            	fac[i]=fac[i-1]*i%Mod;
            HashMap<Integer,Integer> cnt_a=new HashMap<Integer,Integer>();
            HashMap<Integer,Integer> cnt_b=new HashMap<Integer,Integer>();
            HashMap<ArrayList<Integer>,Integer> cnt=new HashMap<ArrayList<Integer>,Integer>();
            Node[] buf=new Node[n];
            for(int i=0;i<n;i++) {
            	int a=sc.nextInt();
            	int b=sc.nextInt();
            	buf[i]=new Node(a,b);
            	int d=0;
            	if(cnt_a.containsKey(a))
            		d=cnt_a.get(a);
            	cnt_a.put(a, d+1);
            	d=0;
            	if(cnt_b.containsKey(b))
            		d=cnt_b.get(b);
            	cnt_b.put(b, d+1);
            	ArrayList<Integer> res=new ArrayList<Integer>(2);
            	res.add(a);
            	res.add(b);
            	d=0;
            	if(cnt.containsKey(res))
            		d=cnt.get(res);
            	cnt.put(res, d+1);
            }
            Arrays.sort(buf);
            long ans=0;
            long s=1;
            for(Map.Entry<Integer, Integer> temp:cnt_a.entrySet()) {
            	s*=fac[temp.getValue()];
            	s%=Mod;
            }
           
            ans=(ans+s%Mod)%Mod;
            s=1;
            for(Map.Entry<Integer, Integer> temp:cnt_b.entrySet()) {
            	s*=fac[temp.getValue()];
            	s%=Mod;
            }
            ans=(ans+s%Mod)%Mod;

            s=1;
            for(Map.Entry<ArrayList<Integer>, Integer> temp:cnt.entrySet()) {
            	s*=fac[temp.getValue()];
            	s%=Mod;
            }
         
            boolean jud=true;
        	for(int i=1;i<n;i++) {
        		if(buf[i].a<buf[i-1].a||buf[i].b<buf[i-1].b) {
        			jud=false;
        			break;
        		}
        	}
        	if(jud) {
        		ans=(ans-s+Mod)%Mod;
        	}
            ans=(fac[n]-ans+Mod)%Mod;
            out.println(ans);
        }
    }
    
    static class Node implements Comparable<Node> {
    	int a;
    	int b;
    	
    	public Node(int a,int b) {
    		this.a=a;
    		this.b=b;
    	}

		@Override
		public int compareTo(Node o) {
			if(this.a!=o.a)
				return this.a-o.a;
			return this.b-o.b;
		}
    }
    
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}
