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.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Objects;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author John Martin
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DNumberOfPermutations solver = new DNumberOfPermutations();
        solver.solve(1, in, out);
        out.close();
    }

    static class DNumberOfPermutations {
        long[] fact;
        long m = 998244353;

        public void solve(int testNumber, InputReader c, OutputWriter w) {
            int n = c.readInt();
            fact = new long[n + 1];
            fac();
            pair a[] = new pair[n];
            for (int i = 0; i < n; i++) {
                a[i] = new pair(c.readInt(), c.readInt());
            }
            pair b[] = a.clone();
            Arrays.sort(a, new Comparator<pair>() {
                public int compare(pair o1, pair o2) {
                    return o1.a - o2.a;
                }
            });
            Arrays.sort(b, new Comparator<pair>() {
                public int compare(pair o1, pair o2) {
                    return o1.b - o2.b;
                }
            });
            long res = fact[n];
            long sub1 = 1;
            for (int i = 0; i < n; i++) {
                int check = a[i].a;
                int cnt = 0;
                while (i < n && a[i].a == check) {
                    i++;
                    cnt++;
                }
                if (i != n - 1 || a[i].a != a[i - 1].a) {
                    i--;
                }
                sub1 *= fact[cnt];
                sub1 %= m;
            }
            res = ((res + m) - sub1) % m;
//        w.printLine(sub1);
            sub1 = 1;
            for (int i = 0; i < n; i++) {
                int check = b[i].b;
                int cnt = 0;
                while (i < n && b[i].b == check) {
                    i++;
                    cnt++;
                }
                if (i != n - 1 || b[i].b != b[i - 1].b) {
                    i--;
                }
                sub1 *= fact[cnt];
                sub1 %= m;
            }
            res = ((res + m) - sub1) % m;


            Arrays.sort(b, new Comparator<pair>() {
                public int compare(pair o1, pair o2) {
                    if (o1.a == o2.a) {
                        return o1.b - o2.b;
                    }
                    return o1.a - o2.a;
                }
            });
            sub1 = 1;
            for (int i = 0; i < n; i++) {
                int check1 = b[i].b;
                int check2 = b[i].a;
                int cnt = 1;
                i++;
                while (i < n && b[i].b == check1 && b[i].a == check2) {
                    i++;
                    cnt++;
                }
                if (i < n && b[i].b < b[i - 1].b) {
                    sub1 = 0;
                }
                if (i != n - 1 || b[i].b != b[i - 1].b) {
                    i--;
                }
                sub1 *= fact[cnt];
                sub1 %= m;
            }
//        w.printLine(sub1);
            res = res + sub1;
            res %= m;


            w.printLine(res);
        }

        private void fac() {
            fact[0] = 1;
            for (int i = 1; i < fact.length; i++) {
                fact[i] = fact[i - 1] * i;
                fact[i] %= m;
            }
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

    }

    static class pair {
        int a;
        int b;

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

        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }
            pair pair = (pair) o;
            return a == pair.a &&
                    b == pair.b;
        }

        public int hashCode() {
            return Objects.hash(a, b);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

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

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

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

