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 CP {
    public static void main(String[] args) throws Exception {
        /*new Thread(null, new Runnable() {
            @Override
            public void run() {
                try {
                    new Solver().solve();
                } catch (Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }, "Solver", 1l << 30).start();*/

        new Solver().solve();
    }
}

class Solver {
    IO io = new IO(System.in, System.out);
    final int MAXN = 1000_006;
    final long MOD = 998244353l;

    final long[] fact;
    Solver() {
        fact = new long[MAXN];
        fact[0] = 1;
        for (int i = 1; i < MAXN; ++i) fact[i] = fact[i - 1] * i % MOD;
    }


    int N;
    long[][] A;
    TreeMap<Long, ArrayList<Long>> P1, P2;

    void solve() throws Exception {
        int i, j, k;

        N = io.nextInt();
        A = new long[N][];
        P1 = new TreeMap<>();
        P2 = new TreeMap<>();
        for (i = 0; i < N; ++i) {
            long a = io.nextLong(), b = io.nextLong();
            A[i] = new long[] {a, b};

            P1.putIfAbsent(a, new ArrayList<>());
            P1.get(a).add(b);

            P2.putIfAbsent(b, new ArrayList<>());
            P2.get(b).add(a);
        }


        for (ArrayList<Long> itr : P1.values()) Collections.sort(itr);
        for (ArrayList<Long> itr : P2.values()) Collections.sort(itr);


        boolean ok = true;
        for (long key : P1.keySet()) if (key > P1.firstKey()) {
            long lower = P1.lowerKey(key);
            ArrayList<Long> ar = P1.get(lower);
            ok = ok && P1.get(key).get(0) >= ar.get(ar.size() - 1);
        }

        long allFirst = 0, allSecond = 0, intersection = 0;
        if (ok) {
            intersection = 1;
            for (long key : P1.keySet()) {
                intersection = intersection * shuffle(P1.get(key)) % MOD;
            }
        }

        allFirst = 1;
        for (long key : P1.keySet()) {
            allFirst = allFirst * fact[P1.get(key).size()] % MOD;
        }

        allSecond = 1;
        for (long key : P2.keySet()) {
            allSecond = allSecond * fact[P2.get(key).size()] % MOD;
        }

        long ans = allFirst + allSecond - intersection;
        ans = fact[N] - ans;
        ans = (ans % MOD + MOD) % MOD;
        io.println(ans);

        io.flush();
    }

    long shuffle(ArrayList<Long> ar) {
        long ret = 1, last = -7; int c = 0;
        for (long itr : ar) {
            if (itr != last) {
                ret = ret * fact[c] % MOD;
                c = 1;
                last = itr;
            } else ++c;
        }
        ret = ret * fact[c] % MOD;
        return ret;
    }
}


class IO {
    static byte[] buf = new byte[2048];
    static int index, total;
    static InputStream in;
    static BufferedWriter bw;


    IO(InputStream is, OutputStream os) {
        try {
            in = is;
            bw = new BufferedWriter(new OutputStreamWriter(os));
        } catch (Exception e) {
        }
    }

    IO(String inputFile, String outputFile) {
        try {
            in = new FileInputStream(inputFile);
            bw = new BufferedWriter(new OutputStreamWriter(
                    new FileOutputStream(outputFile)));
        } catch (Exception e) {
        }
    }

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

    String next() throws Exception {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan())
            sb.append((char) c);
        return sb.toString();
    }

    int nextInt() throws Exception {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+')
            c = scan();
        for (; c >= '0' && c <= '9'; c = scan())
            val = (val << 3) + (val << 1) + (c & 15);
        return neg ? -val : val;
    }

    long nextLong() throws Exception {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+')
            c = scan();
        for (; c >= '0' && c <= '9'; c = scan())
            val = (val << 3) + (val << 1) + (c & 15);
        return neg ? -val : val;
    }

    void print(Object a) throws Exception {
        bw.write(a.toString());
    }

    void printsp(Object a) throws Exception {
        print(a);
        bw.write(" ");
    }

    void println() throws Exception {
        bw.write("\n");
    }

    void println(Object a) throws Exception {
        print(a);
        println();
    }

    void flush() throws Exception {
        bw.flush();
        bw.close();
    }
}