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.util.*;
import java.io.*;

public class D71 {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        long mod = 998244353;
        long n = sc.nextLong();
        Pair [] p = new Pair[(int)n]; for (int i = 0; i < n; i++) p[i] = new Pair(sc.nextInt(), sc.nextInt());
        Map<Integer, Integer> first = new HashMap<>();
        Map<Integer, Integer> second = new HashMap<>();
        for (int i = 0; i < n; i++) {
            first.put(p[i].x, first.getOrDefault(p[i].x, 0) + 1);
            second.put(p[i].y, second.getOrDefault(p[i].y, 0) + 1);
        }
        fac = new long[(int)n + 4];
        initFac(n + 2);
        long badFirst = 1; long badSecond = 1;
        for (Integer x: first.keySet()) {
            badFirst = (badFirst * fac[first.get(x)]) % mod;
        }
        for (Integer x: second.keySet()) {
            badSecond = (badSecond * fac[second.get(x)]) % mod;
        }
        Arrays.sort(p);
        boolean ok = true;
        for (int i = 0; i < n - 1; i++) {
            ok &= (p[i].x <= p[i + 1].x);
            ok &= (p[i].y <= p[i + 1].y);
        }
        if (ok) {
            Map<Pair, Integer> map = new HashMap<>();
            for (int i = 0; i < n;i++) map.put(p[i], map.getOrDefault(p[i], 0) + 1);
            long sub = 1;
            for (Pair m: map.keySet()) {
                sub = (sub * fac[map.get(m)]) % mod;
            }
            long ans = (fac[(int) n] - (badFirst + badSecond) % mod) % mod;
            ans = (ans + sub) % mod;
            if (ans < 0) ans += mod;
            out.println(ans);
        } else {
            long ans = (fac[(int) n] - (badFirst + badSecond) % mod) % mod;
            if (ans < 0) ans += mod;
            out.println(ans);
        }
        out.close();
    }

    static class Pair implements Comparable<Pair> {
        int x; int y;
        Pair (int x, int y) {
            this.x = x; this.y = y;
        }

        @Override
        public int compareTo(Pair o) {
            if (x - o.x == 0) return Integer.compare(y, o.y);
            return Integer.compare(x, o.x);
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return x == pair.x &&
                    y == pair.y;
        }

        @Override
        public int hashCode() {
            return Objects.hash(x, y);
        }
    }

    static long[] fac;
    static int mod = 998244353;

    static void initFac(long n) {
        fac[0] = 1;
        for (int i = 1; i <= n; i++) {
            fac[i] = (fac[i - 1]  * i) % mod;
        }
    }

    static long exponentiation(long base, long exp)
    {
        long t = 1L;
        while (exp > 0) {

            // for cases where exponent
            // is not an even value
            if (exp % 2 != 0)
                t = (t * base) % mod;

            base = (base * base) % mod;
            exp /= 2;
        }
        return t % mod;
    }

    static long nck(int n, int k) {
        if (n < k)
            return 0;
        long den = inv((int) (fac[k] * fac[n - k] % mod));
        return fac[n] * den % mod;
    }

    static int pow(long b, int e) {
        long ans = 1;
        while (e > 0) {
            if (e % 2 == 1)
                ans = ans * b % mod;
            e >>= 1;
            b = b * b % mod;
        }
        return (int) ans;
    }

    static int inv(int x) {
        return pow(x, mod - 2);
    }



    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}