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. 
/**
 * Created at 04:24 on 2019-08-23
 */

import java.io.*;
import java.util.*;

/*
 * 場合の数
 */

public class Main {

  static FastScanner sc = new FastScanner();
  static Output out = new Output(System.out);

  static final int[] dx = {0, 1, 0, -1};
  static final int[] dy = {-1, 0, 1, 0};

  static final long MOD = 998244353L;
  static final long INF = Long.MAX_VALUE / 2;

  public static class Solver {
    public Solver() {

      int N = sc.nextInt();

      long[] countA = new long[N+1];
      long[] countB = new long[N+1];

      Data[] data = new Data[N];
      for (int i=0; i<N; i++) {
        data[i] = new Data(sc.nextInt(), sc.nextInt());
        countA[data[i].a]++;
        countB[data[i].b]++;
      }

      new Mod(N);

      long ans = Mod.factorial(N);

      long count = 1;
      for (int i=1; i<=N; i++) {
        count = Mod.mul(count, Mod.factorial(countA[i]));
      }

      ans = Mod.sub(ans, count);

      count = 1;
      for (int i=1; i<=N; i++) {
        count = Mod.mul(count, Mod.factorial(countB[i]));
      }

      ans = Mod.sub(ans, count);


      Arrays.sort(data, (o1, o2) -> {
        if (o1.a == o2.a) return o1.b - o2.b;
        else return o1.a - o2.a;
      });

      count = 1;
      /*
      long sameCount = 1;
      for (int p=1; p<=N; p++) {

        if (p == N || data[p].a != data[p-1].a) {
          count = Mod.mul(count, Mod.factorial(sameCount));
          sameCount = 1;
          if (p < N && data[p].b < data[p-1].b) {
            count = 0;
            break;
          }
        } else {
          if (data[p].b  != data[p-1].b) {
            count = Mod.mul(count, Mod.factorial(sameCount));
            sameCount = 1;
          } else {
            sameCount++;
          }
        }


      }*/

      int l = 0, r = 1;
      while (l < N) {
        while (r < N && data[r].a == data[r-1].a && data[r].b == data[r-1].b) r++;

        if (r < N && data[r].a != data[r-1].a && data[r].b < data[r-1].b) {
          count = 0;
          break;
        }
        count = Mod.mul(count, Mod.factorial(r-l));
        l = r;
        r++;
      }

      ans = Mod.add(ans, count);

      out.println(ans);

    }

    class Data {
      int a, b;
      Data(int l, int r) {
        a = l;
        b = r;
      }
    }


    public static class Mod {

      public static long[] fact;

      public Mod(int n) {
        fact = new long[n+1];
      }

      public Mod(long n) {
        fact = new long[(int)n+1];
      }

      public static long comb(long n, long r) {
        if (r < 0 || r > n) return 0;
        return (((factorial(n) * factorialInverse(r)) % MOD) * factorialInverse(n - r)) % MOD;
      }

      public static long factorial(long n) {
        if (n == 0) return 1;
        if (fact[(int) n] == 0) {
          return fact[(int) n] = (n * factorial(n - 1)) % MOD;
        } else {
          return fact[(int) n];
        }
      }

      public static long factorialInverse(long n) {
        return inverse(factorial(n));
      }

      public static long inverse(long n) {
        return power(n, MOD - 2);
      }

      public static long power(long a, long b) {
        if (b == 0) return 1;

        if (b % 2 == 0) {
          long p = power(a, b / 2);
          return (p * p) % MOD;
        } else {
          return (a * power(a, b - 1)) % MOD;
        }
      }

      public static long add(long... a) {
        long ans = 0;
        for (int i=0; i<a.length; i++) {
          ans = (ans + a[i]) % MOD;
        }
        return ans;
      }

      public static long sub(long a, long b) {
        return (a - b + MOD) % MOD;
      }

      public static long mul(long... a) {
        long ans = 1;
        for (int i=0; i<a.length; i++) {
          ans = (ans * a[i]) % MOD;
        }
        return ans;
      }

      public static long div(long a, long b) {
        return (a * Mod.inverse(b)) % MOD;
      }

    }
  }

  public static void main(String[] args) {
    new Solver();
    out.flush();
  }

  static class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private boolean hasNextByte() {
      if (ptr < buflen) {
        return true;
      } else {
        ptr = 0;
        try {
          buflen = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (buflen <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) return buffer[ptr++];
      else return -1;
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    public boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    public long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int N, boolean oneBased) {
      if (oneBased) {
        int[] array = new int[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      } else {
        int[] array = new int[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      }
    }

    public long[] nextLongArray(int N, boolean oneBased) {
      if (oneBased) {
        long[] array = new long[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      } else {
        long[] array = new long[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      }
    }
  }

  static class Output extends PrintWriter {

    public Output(PrintStream ps) {
      super(ps);
    }

    public void print(int[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(long[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(String[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(ArrayList a, String separator) {
      for (int i = 0; i < a.size(); i++) {
        if (i == 0) print(a.get(i));
        else print(separator + a.get(i));
      }
      println();
    }
  }

}
