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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.util.Random;
import java.util.Comparator;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DNumberOfPermutations solver = new DNumberOfPermutations();
        solver.solve(1, in, out);
        out.close();
    }

    static class DNumberOfPermutations {
        long mod = 998244353;

        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int[][] ar = new int[n][2];
            for (int i = 0; i < n; i++) {
                ar[i][0] = in.scanInt();
                ar[i][1] = in.scanInt();
            }
            long[] factorial = new long[n + 1];
            factorial[0] = 1;
            for (int i = 1; i <= n; i++) factorial[i] = (factorial[i - 1] * i) % mod;
            CodeHash.shuffle(ar);
            Arrays.sort(ar, new Comparator<int[]>() {

                public int compare(int[] o1, int[] o2) {
                    return o1[0] - o2[0];
                }
            });
            long ans = factorial[n];
            long temp1 = 1;
            for (int i = 0; i < n; ) {
                int temp = i;
                while (temp < n && ar[temp][0] == ar[i][0]) temp++;
                temp1 = (temp1 * factorial[temp - i]) % mod;
                i = temp;
            }
            CodeHash.shuffle(ar);
            Arrays.sort(ar, new Comparator<int[]>() {

                public int compare(int[] o1, int[] o2) {
                    return o1[1] - o2[1];
                }
            });
            long temp2 = 1;
            for (int i = 0; i < n; ) {
                int temp = i;
                while (temp < n && ar[temp][1] == ar[i][1]) temp++;
                temp2 = (temp2 * factorial[temp - i]) % mod;
                i = temp;
            }

            CodeHash.shuffle(ar);
            Arrays.sort(ar, new Comparator<int[]>() {

                public int compare(int[] o1, int[] o2) {
                    if (o1[0] == o2[0]) return o1[1] - o2[1];
                    return o1[0] - o2[0];
                }
            });
            long temp3 = 1;
            for (int i = 0; i < n; ) {
                int temp = i;
                while (temp < n && ar[temp][1] == ar[i][1] && ar[temp][0] == ar[i][0]) temp++;
                temp3 = (temp3 * factorial[temp - i]) % mod;
                i = temp;
            }
            for (int i = 1; i < n; i++) {
                if (!(ar[i][0] >= ar[i - 1][0] && ar[i][1] >= ar[i - 1][1])) temp3 = 0;
            }
            long sub = temp1 + temp2 - temp3;
            sub %= mod;
            while (sub < 0) sub += mod;
            ans -= sub;
            while (ans < 0) ans += mod;
            ans %= mod;
            out.println(ans);

        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }

    static class CodeHash {
        public static void shuffle(int[][] ar) {
            Random rd = new Random(new Random().nextInt());
            for (int i = 0; i < ar.length; i++) {
                int index = rd.nextInt(ar.length);
                int[] temp = ar[i];
                ar[i] = ar[index];
                ar[index] = temp;
            }
        }

    }
}

