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.*;
import java.lang.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.*;
import java.math.*;
public class Main { 
        public long fact(long n) {
            if(n==0) {
                return 1%998244353;
            }
            else return ((n%998244353)*(fact(n-1)%998244353))%998244353;
        }
    public static void main(String[] args) throws Exception{
        Reader.init(System.in);
        PrintWriter out = new PrintWriter(System.out);
        Main mm=new Main();
        int n=Reader.nextInt();
        HashMap<Integer,Integer> m1=new HashMap<Integer,Integer>();
        HashMap<Integer,Integer> m2=new HashMap<Integer,Integer>();
        long ans1=1;
        long ans2=1;
        ArrayList<node> list=new ArrayList<node>();
        for(int i=0;i<n;i++) {
            int a=Reader.nextInt();
            int b=Reader.nextInt();
            list.add(new node(a,b));
            if(m1.containsKey(a)) {
                int temp=m1.get(a);
                ans1*=(temp+1)%998244353;
                ans1%=998244353;
                m1.put(a, temp+1);
            }
            else {
                m1.put(a,1);
            }
            if(m2.containsKey(b)) {
                int temp=m2.get(b);
                ans2*=(temp+1)%998244353;
                ans2%=998244353;
                m2.put(b, temp+1);
            }
            else {
                m2.put(b,1);
            }
        }
        //out.println(ans1+ans2);
        Collections.sort(list,new a());
        long dup=1;
        long prev=1;
        long flag=1;
        for(int i=1;i<n;i++) {
            if(list.get(i-1).a==list.get(i).a && list.get(i-1).b==list.get(i).b) {
                prev++;
            }
            else {
                dup*=mm.fact(prev);
                dup%=998244353;
                prev=1;
            }
            if(list.get(i).b<list.get(i-1).b) {
                flag=0;
            }
        }
        dup*=mm.fact(prev);
        dup%=998244353;
        if(flag==1) {
            out.println((mm.fact(n)-(ans1+ans2-dup)%998244353+998244353)%998244353);
        }
        else {
            out.println((mm.fact(n)-(ans1+ans2)%998244353+998244353)%998244353);
        }
        out.close();}
}
class node {
    int a;
    int b;
    node(int a,int b){
        this.a=a;
        this.b=b;
    }
}
class a implements Comparator<node>{
    public int compare(node n1,node n2) {
        if(n1.a==n2.a) {
            return n1.b-n2.b;
        }
        else {
            return n1.a-n2.a;
        }
    }
}
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
    /** call this method to initialize reader for InputStream */
    static void init() throws IOException {
         reader = new BufferedReader(
                 new FileReader("input.txt"));
    tokenizer = new StringTokenizer("");
    }
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    /** get next word */
    static String nextLine() throws IOException{
        return reader.readLine();
    }
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }
    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}