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.*;
import java.math.BigInteger;
import java.util.*;
public class Main {
    static StreamTokenizer in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
    static BufferedReader buffer = new BufferedReader(new InputStreamReader(System.in));
    static Scanner sc = new Scanner(System.in);
    static InputReader input=new InputReader(System.in);
    static PrintWriter out = new PrintWriter(System.out);
    static int mod=998244353;
    static final int maxn=(int)3e5+10;
    static P p[]=new P[maxn];
    static long jie[]=new long[maxn];
    static int bu1[]=new int[maxn];
    static int bu2[]=new int[maxn];

    public static void main(String args[]) throws Exception{
        jie[0]=1;
        jie[1]=1;
        for(int i=2;i<maxn;i++)jie[i]=(jie[i-1]*i)%mod;
        int n=getInt();
        long ans=jie[n],sub1=1,sub2=1,add=1;

        for(int i=0;i<n;i++)
        {
            p[i]=new P(getInt(),getInt());
            bu1[p[i].x]++;
            bu2[p[i].y]++;
        }
        Arrays.sort(p,0,n);
        for(int i=0;i<=n;i++)
        {
            sub1*=jie[bu1[i]];
            sub1%=mod;
            sub2*=jie[bu2[i]];
            sub2%=mod;
        }

        for(int i=0;i<n-1;i++)
            if(p[i].y>p[i+1].y)
                add=0;

        if(add!=0)
        {
            int cnt=1;
            for(int i=1;i<n;i++)
            {
                if(p[i].x==p[i-1].x&&p[i].y==p[i-1].y)
                {
                    cnt++;
                }
                else
                {
                    add*=jie[cnt];
                    add%=mod;
                    cnt=1;
                }
            }
            add*=jie[cnt];
            add%=mod;
        }

        ans-=sub1+sub2;
        ans+=add;
        ans+=mod*2;
        ans%=mod;
        System.out.println(ans);
    }
    static int getInt()throws Exception{
        in.nextToken();
        return (int)in.nval;
    }
}
class P implements Comparable{
    int x,y;
    public P(int a,int b){
        x=a;y=b;
    }
    public int compareTo(Object O){
        P n=(P)O;
        if(n.x==x)return this.y-n.y;
        return this.x-n.x;
    }
}
class InputReader {

    private final InputStream stream;
    private final byte[] buf = new byte[8192];
    private int curChar, snumChars;

    public InputReader(InputStream st) {
        this.stream = st;
    }

    public int read() {
        if (snumChars == -1)
            throw new InputMismatchException();
        if (curChar >= snumChars) {
            curChar = 0;
            try {
                snumChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (snumChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int nextInt() {
        int c = read();
        while (isSpaceChar(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public long nextLong() {
        int c = read();
        while (isSpaceChar(c)) {
            c = read();
        }
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public int[] nextIntArray(int n) {
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    public String readString() {
        int c = read();
        while (isSpaceChar(c)) {
            c = read();
        }
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public String nextLine() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndOfLine(c));
        return res.toString();
    }

    public boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private boolean isEndOfLine(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }
}
