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 javafx.util.Pair;

import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException{

        Locale.setDefault(Locale.US);
        //----------------CODE HERE-------------------
        int n;
        n = sc.nextInt();

        ArrayList<Node> nodes = new ArrayList<>();
        ArrayList<NodeA> nodesA = new ArrayList<>();
        ArrayList<NodeB> nodesB = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            nodes.add(new Node(a, b));
            nodesA.add(new NodeA(a, b));
            nodesB.add(new NodeB(a, b));
        }

        Collections.sort(nodes);
        Collections.sort(nodesA);
        Collections.sort(nodesB);

        ArrayList<Integer> dupes = new ArrayList<>();
        ArrayList<Integer> dupesA = new ArrayList<>();
        ArrayList<Integer> dupesB = new ArrayList<>();
        int d = 1;
        int da = 1;
        int db = 1;
        for (int i = 1; i < n; i++) {
            if (nodes.get(i).compareTo(nodes.get(i-1)) == 0) {
                d++;
            }
            else {
                dupes.add(d);
                d = 1;
            }
            if (nodesA.get(i).compareTo(nodesA.get(i-1)) == 0) {
                da++;
            }
            else {
                dupesA.add(da);
                da = 1;
            }
            if (nodesB.get(i).compareTo(nodesB.get(i-1)) == 0) {
                db++;
            }
            else {
                dupesB.add(db);
                db = 1;
            }
        }
        if (d > 1) {
            dupes.add(d);
        }
        if (da > 1) {
            dupesA.add(da);
        }
        if (db > 1) {
            dupesB.add(db);
        }

        long nFact = 1;
        long totalAB = 1;
        long totalA = 1;
        long totalB = 1;

        for (int i = 1; i < nodes.size(); i++) {
            if(nodes.get(i).a < nodes.get(i-1).a || nodes.get(i).b < nodes.get(i-1).b) {
                totalAB = 0;
                break;
            }
        }
        if (totalAB != 0) {
            totalAB = getTotal(dupes);
        }
        totalA = getTotal(dupesA);
        totalB = getTotal(dupesB);
        for (int i = 1; i <= n; i++) {
            nFact *= i;
            if (nFact > 998244353) {
                nFact %= 998244353;
            }
        }
        nFact -= totalA;
        nFact %= 998244353;
        nFact += totalAB;
        nFact %= 998244353;
        nFact -= totalB;
        nFact %= 998244353;

        while (nFact < 0) {
            nFact+=998244353;
        }
        out.println(nFact);
        //----------------CODE HERE--------------------
        out.flush();
    }

    private static long getTotal(ArrayList<Integer> dupes) {
        long d = 1;
        for (int i = 0; i < dupes.size(); i++) {
            for (int j = 1; j <= dupes.get(i); j++) {
                d *= j;
                if (d > 998244353) {
                    d %= 998244353;
                }
            }
        }
        return d;
    }

    public 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 -1;
            if (this.a > o.a)
                return 1;
            if (this.b < o.b)
                return -1;
            if (this.b > o.b)
                return 1;
            return 0;
        }
    }

    public static class NodeA implements Comparable<NodeA>{
        int a;
        int b;

        public NodeA(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(NodeA o) {
            if (this.a < o.a)
                return -1;
            if (this.a > o.a)
                return 1;
            return 0;
        }
    }

    public static class NodeB implements Comparable<NodeB>{
        int a;
        int b;

        public NodeB(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(NodeB o) {
            if (this.b < o.b)
                return -1;
            if (this.b > o.b)
                return 1;
            return 0;
        }
    }

    //-----------PrintWriter for faster output---------------------------------
    public static MyScanner sc = new MyScanner();
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }

    }
    //--------------------------------------------------------
}
