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.util.*;
import java.util.stream.*;

import static java.lang.Integer.parseInt;

public class m implements Runnable {
  private static final boolean ONLINE_JUDGE = true; //System.getProperty("ONLINE_JUDGE") != null;

  public static void main(String[] args) {
    new Thread(new m()).start();
  }

  @Override
  public void run() {
    try (BufferedReader reader = ONLINE_JUDGE ? new BufferedReader(new InputStreamReader(System.in))
                                              : new BufferedReader(new FileReader("input"));
         Writer writer = ONLINE_JUDGE ? new OutputStreamWriter(System.out) : new FileWriter("output");
         PrintWriter printWriter = new PrintWriter(writer);) {
      Solver solver = new Solver(reader, printWriter);
      while (solver.solve());
    } catch (IOException e) {
      e.printStackTrace(System.err);
    }
  }

  static final class Solver {
    static final long mod = 998244353;
    final BufferedReader in;
    final PrintWriter out;

    long[] fact;
    long[] invfact;

    public Solver(BufferedReader reader, PrintWriter writer) {
      in = reader;
      out = writer;
    }

    long fact(int n) {
      long res = 1;
      for (int i = 2; i < n; ++i) {
        res = (res * n) % mod;
      }
      return res;
    }

    long pow(long a, int n) {
      if (n == 1) return a % mod;
      long res = pow(a, n >> 1);
      if (n % 2 == 0) {
        return (res * res) % mod;
      }
      return (a * (res * res) % mod ) % mod;
    }

    boolean solve() throws IOException {
      String line = in.readLine();
      if (line == null) {
        return false;
      }
      if (line.isEmpty()) {
        return true;
      }

      
      StringTokenizer tok = new StringTokenizer(line);
      int n = parseInt(tok.nextToken());
      List<Pair> nums = new ArrayList<>(n);
      for (int i = 0; i < n; ++i) {
        tok = new StringTokenizer(in.readLine());
        int x = parseInt(tok.nextToken());
        int y = parseInt(tok.nextToken());
        nums.add(new Pair(x, y));
      }
      if (n == 1) {
        out.println(0);
        return true;
      }

      nums.sort(Comparator.comparing(Pair::getY));
      List<Integer> idy = new ArrayList<>();
      for (int i = 1; i < nums.size(); ++i) {
        int id = 1;
        while (i < nums.size() && nums.get(i).getY() == nums.get(i - 1).getY()) {
          ++i;
          ++id;
        }
        //debug("found y " + id);
        if (id > 1)  idy.add(id);
      }
      nums.sort(Comparator.comparing(Pair::getX).thenComparing(Pair::getY));
      List<Integer> idx = new ArrayList<>();
      for (int i = 1; i < nums.size(); ++i) {
        int id = 1;
        while (i < nums.size() && nums.get(i).getX() == nums.get(i - 1).getX()) {
          ++i;
          ++id;
        }
        //debug("found x " + id);
        if (id > 1)  idx.add(id);
      }
      boolean xysorted = true;
      for (int i = 1; i < nums.size(); ++i) {
        if (nums.get(i).getY() < nums.get(i - 1).getY()) {
          xysorted = false;
          break;
        }
      }
      List<Integer> idxy = new ArrayList<>();
      if (xysorted) {
        for (int i = 1; i < nums.size(); ++i) {
          int id = 1;
          while (i < nums.size() && nums.get(i).getX() == nums.get(i - 1).getX() && nums.get(i).getY() == nums.get(i - 1).getY()) {
            ++i;
            ++id;
          }
          //debug("found x y " + id);
          if (id > 1)  idxy.add(id);
        }
      }


      long[] fact = new long[n + 1];
      fact[0] = fact[1] = 1;
      for (int i = 2; i <= n; ++i) {
        fact[i] = (fact[i - 1] * i) % mod;
      }

      long total = (((((fact[n] + (xysorted ? multfacts(fact, idxy) : 0)) % mod) + mod - multfacts(fact, idx)) % mod) + mod - multfacts(fact, idy)) % mod;
      out.println(total % mod);

      return true;
    }

    long multfacts(long[] fact, List<Integer> list) {
      long res = 1;
      for (Integer elem : list) {
        res = (res * fact[elem]) % mod;
      }
      return res;
    }

    class Pair {
      int x;
      int y;
      Pair(int xx, int yy) {
        x =xx;
        y = yy;
      }

      int getX() {return x;}
      int getY() {return y;}
    }
  }

  static void debug(String s) {
    System.out.println(s);
  }
}
