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. 

/*
 * @author romit17
 */

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;

public class D1207 {
    
    void solve() throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        StringBuilder sb = new StringBuilder("");
        long mod = 998244353;
        long[] fact = new long[300005];
        fact[0] = fact[1] = 1;
        for(int i=2;i<300005;i++)
            fact[i] = (fact[i-1]*i)%mod;
        
        int n = ni();
        data[] a = new data[n];
        HashMap<Integer, Integer> h1 = new HashMap<>();
        HashMap<Integer, Integer> h2 = new HashMap<>();
        
        for(int i=0;i<n;i++)
        {
            int x = ni(), y = ni();
            a[i] = new data(x, y);
            h1.put(x, h1.getOrDefault(x, 0)+1);
            h2.put(y, h2.getOrDefault(y, 0)+1);
        }
        long res1 = 1;
        long res2 = 1;
        long res3 = 0;
        for(int i:h1.values())
            res1 = (res1*fact[i])%mod;
        for(int i:h2.values())
            res2 = (res2*fact[i])%mod;
        
        Arrays.sort(a);
        boolean fg = true;
        for(int i=0;i<n-1;i++)
        {
            if(a[i].b > a[i+1].b)
            {
                fg = false; break;
            }
        }
        
        if(fg)
        {
            res3 = 1;
            HashMap<Long, Integer> h3 = new HashMap<>();
            for(data d:a)
            {
                long x = d.a;
                long y = d.b;
                x = x*1000000+y;
                h3.put(x, h3.getOrDefault(x, 0)+1);
            }
            for(int i:h3.values())
                    res3 = (res3*fact[i])%mod;
        }
        long res = (((fact[n] - res1)%mod - res2)%mod + res3)%mod;
        res = (res+mod)%mod;
        System.out.println(res);
    }
    
    public class data implements Comparable<data>
    {
        int a;
        int b; 

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

        @Override
        public int compareTo(data o) {
            if(this.a == o.a) return this.b-o.b;
            return this.a-o.a;
        }
        
    }
    
    public static void main(String[] args) throws IOException {
        new D1207().solve();
    }    
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;    
    InputStream is = System.in;

    private int readByte() {
        if (lenbuf == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) {
                return -1;
            }
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }
    
    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }
    
    private double nd() {
        return Double.parseDouble(ns());
    }
    
    private char nc() {
        return (char) skip();
    }
    
    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) {
            map[i] = ns(m);
        }
        return map;
    }
    
    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }
    
    private int[] na1(int n) {
        int[] a = new int[n + 1];
        for (int i = 1; i < n + 1; i++) {
            a[i] = ni();
        }
        return a;
    }
    
    private long[] nb(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nl();
        }
        return a;
    }
    
    private long[] nb1(int n) {
        long[] a = new long[n + 1];
        for (int i = 1; i < n + 1; i++) {
            a[i] = nl();
        }
        return a;
    }
    
    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
}

