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. 
// package Quarantine;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class NumberOfPermutations {
    static long fact[];
    static int mod;
    public static void main(String[] args)throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        mod=998244353;
        fact=new long[n+1];
        fact[0]=1;
        for(int i=1;i<=n;i++){
            fact[i]=(fact[i-1]*i)%mod;
        }
//        int a[]=new int[n];
//        int b[]=new int[n];
        long ans=fact[n];
//        PermPair p[]=new PermPair[n];
        ArrayList<Integer> a=new ArrayList<>();
        ArrayList<Integer> b=new ArrayList<>();
        ArrayList<PermPair> p=new ArrayList<>();
        for(int i=0;i<n;i++){
            StringTokenizer st=new StringTokenizer(br.readLine());
            int x=Integer.parseInt(st.nextToken());
            int y=Integer.parseInt(st.nextToken());
            a.add(x);
            b.add(y);
            p.add(new PermPair(x,y));
        }
        Collections.sort(a);
        Collections.sort(b);
        Collections.sort(p);
        ans=(ans-getAns(a)+mod)%mod;
        ans=(ans-getAns(b)+mod)%mod;
//        print(p);
        if(check(p)){
            long temp=1;
            for(int i=0;i<n;){
                int count=1;
                while(i+1<n){
                    PermPair curr=p.get(i);
                    PermPair next=p.get(i+1);
                    int fcurr=curr.f,scurr=curr.s;
                    int fnext=next.f,snext=next.s;
                    if(fcurr==fnext&&scurr==snext) {
                        count++;
                        i++;
                    }
                    else{
                        break;
                    }
                }
//                System.out.println(count+" "+i);
//                if(count==1)
                i++;
                temp=(temp*fact[count])%mod;
            }
//            System.out.println(temp);
            ans=(ans+temp)%mod;
        }
        System.out.println(ans);
    }
    public static void print(PermPair a[]){
        for(int i=0;i<a.length;i++){
            System.out.println(a[i].f+" "+a[i].s);
        }
    }
    public static boolean check(ArrayList<PermPair> p){
        for(int i=1;i<p.size();i++){
            int curr=p.get(i).s;
            int prev=p.get(i-1).s;
            if(curr<prev){
                return false;
            }
        }
        return true;
    }
    public static long getAns(ArrayList<Integer> a){
        long ans=1;
        for(int i=0;i<a.size();){
            int count=1;
            while(i+1<a.size()){
                int curr=a.get(i);
                int next=a.get(i+1);
                if(curr==next) {
                    count++;
                    i++;
                }
                else{
                    break;
                }
//                System.out.println(count+" "+i+"xxx");
            }
//            if(count==1)
//            System.out.println(count+" "+i);
            i++;
            ans=(ans*fact[count])%mod;
        }
//        System.out.println(ans);
        return ans;
    }
}

class PermPair implements Comparable<PermPair>{
    int f,s;
    public PermPair(int f,int s){
        this.f=f;
        this.s=s;
    }

    @Override
    public int compareTo(PermPair o) {
        if(this.f!=o.f){
            return this.f-o.f;
        }
        else{
            return this.s-o.s;
        }
    }

}
