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.util.TreeMap;
import java.util.Map;
import java.io.IOException;
import java.util.Comparator;
import java.io.InputStream;

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

    static class DNumberOfPermutations {
        long mod = 998244353;
        int MAXN = 300005;
        PrintWriter out;
        InputReader in;
        long[] fact = new long[MAXN];
        final Comparator<Tuple> com = new Comparator<Tuple>() {
            public int compare(Tuple t1, Tuple t2) {
                if (t1.x != t2.x)
                    return Integer.compare(t1.x, t2.x);
                else
                    return Integer.compare(t1.y, t2.y);
            }
        };

        void pre() {
            int i = 0;
            fact[0] = 1;
            for (i = 1; i < MAXN; i++)
                fact[i] = fact[i - 1] * i % mod;
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            this.out = out;
            this.in = in;
            pre();
            int n = ni();
            TreeMap<Integer, Integer> tmap1 = new TreeMap<>();
            TreeMap<Integer, Integer> tmap2 = new TreeMap<>();
            TreeMap<Tuple, Integer> tmap3 = new TreeMap<>(com);
            Tuple[] arr = new Tuple[n];
            int i = 0;
            for (i = 0; i < n; i++) {
                int a = ni();
                int b = ni();
                tmap1.put(a, tmap1.getOrDefault(a, 0) + 1);
                tmap2.put(b, tmap2.getOrDefault(b, 0) + 1);
                Tuple curr = new Tuple(a, b);
                arr[i] = curr;
                tmap3.put(curr, tmap3.getOrDefault(curr, 0) + 1);
            }
            Arrays.sort(arr, com);
            boolean ok = true;
            for (i = 0; i < n - 1; i++) {
                ok &= arr[i].x <= arr[i + 1].x;
                ok &= arr[i].y <= arr[i + 1].y;
            }
            long ans1 = 1, ans2 = 1, ans3 = 1;
            for (Integer p : tmap1.keySet()) {
                ans1 *= fact[tmap1.get(p)];
                ans1 %= mod;
            }
            for (Integer p : tmap2.keySet()) {
                ans2 *= fact[tmap2.get(p)];
                ans2 %= mod;
            }
            ans1 += ans2;
            ans1 %= mod;
            if (ok) {
                for (Tuple t : tmap3.keySet()) {
                    ans3 *= fact[tmap3.get(t)];
                    ans3 %= mod;
                }
                ans1 -= ans3;
                ans1 += mod;
                ans1 %= mod;
            }
            ans1 = fact[n] - ans1;
            ans1 += mod;
            pn(ans1 % mod);
        }

        int ni() {
            return in.nextInt();
        }

        void pn(long zx) {
            out.println(zx);
        }

        class Tuple {
            int x;
            int y;

            Tuple(int a, int b) {
                x = a;
                y = b;
            }

        }

    }

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

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

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

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

        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));

            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }
}

