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.*;

public class Main {
    FastScanner in;
    PrintWriter out;
    private static final int MODULO = 998244353;

    public static void main(String[] args) {
        (new Main()).run();
    }

    void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            solve();
            in.close();
            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    void solve() throws IOException {
        int n = in.nextInt();
        List<IntPair> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int a = in.nextInt();
            int b = in.nextInt();
            list.add(new IntPair(a, b));
        }
        long p0 = f(n);
        Collections.sort(list, new Comparator<IntPair>() {
            @Override
            public int compare(IntPair intPair, IntPair t1) {
                return Integer.compare(intPair.a, t1.a);
            }
        });
        long p1 = 1;
        int start = -1;
        for (int i = 1; i < list.size(); i++) {
            if (list.get(i).a == list.get(i - 1).a) {
                if (start < 0) {
                    start = i - 1;
                }
            } else {
                if (start >= 0) {
                    p1 *= f(i - start);
                    p1 %= MODULO;
                    start = -1;
                }
            }
        }
        if (start >= 0) {
            p1 *= f(n - start);
            p1 %= MODULO;
        }
        long p2 = 1;
        start = -1;
        Collections.sort(list, new Comparator<IntPair>() {
            @Override
            public int compare(IntPair intPair, IntPair t1) {
                return Integer.compare(intPair.b, t1.b);
            }
        });
        for (int i = 1; i < list.size(); i++) {
            if (list.get(i).b == list.get(i - 1).b) {
                if (start < 0) {
                    start = i - 1;
                }
            } else {
                if (start >= 0) {
                    p2 *= f(i - start);
                    p2 %= MODULO;
                    start = -1;
                }
            }
        }
        if (start >= 0) {
            p2 *= f(n - start);
            p2 %= MODULO;
        }
        Collections.sort(list, new Comparator<IntPair>() {
            @Override
            public int compare(IntPair intPair, IntPair t1) {
                return intPair.a == t1.a ? Integer.compare(intPair.b, t1.b) : Integer.compare(intPair.a, t1.a);
            }
        });
        boolean sorted = true;
        for (int i = 1; i < n; i++) {
            sorted &= (list.get(i).b >= list.get(i - 1).b);
            sorted &= (list.get(i).a >= list.get(i - 1).a);
        }
        long p12 = sorted ? 1 : 0;
        start = -1;
        for (int i = 1; i < list.size(); i++) {
            if (list.get(i).a == list.get(i - 1).a && list.get(i).b == list.get(i - 1).b) {
                if (start < 0) {
                    start = i - 1;
                }
            } else {
                if (start >= 0) {
                    p12 *= f(i - start);
                    p12 %= MODULO;
                    start = -1;
                }
            }
        }
        if (start >= 0) {
            p12 *= f(n - start);
            p12 %= MODULO;
        }
        //System.err.println(p0 + " " + p1 + " " + p2 + " " + p12);
        out.println((p0 - p1 - p2 + p12 + 2L * MODULO) % MODULO);
    }

    private static long f(int n) {
        long total = 1;
        for (int i = 1; i <= n; i++) {
            total *= i;
            total %= MODULO;
        }
        return total;
    }

    private static class IntPair {
        int a;
        int b;

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

        @Override
        public String toString() {
            return a + " " + b;
        }
    }

    private static class FastScanner {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        FastScanner(InputStream inputStream) {
            bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        }

        String next() throws IOException {
            while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                String line = bufferedReader.readLine();
                if (line == null) return null;
                stringTokenizer = new StringTokenizer(line);
            }
            return stringTokenizer.nextToken();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        void close() throws IOException {
            bufferedReader.close();
            ;
        }
    }
}
