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.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.util.Comparator;

public class Main {
    interface OrderChecker {
        boolean check(int a, int b);
    }

    private static final long MOD = 998244353;
    private static final long[] fact;

    static {
        int n = (int)3.2e5;
        fact = new long[n];
        fact[0] = 1;
        for (int i = 1; i < n; ++i)
            fact[i] = (fact[i-1] * i) % MOD;
    }

    private static long cntBadBy(int n, Comparator<Integer> c, OrderChecker t) {
        Integer[] perm = new Integer[n];
        for (int i = 0; i < n; i++)
            perm[i] = i;
        Arrays.sort(perm, c);
        if (t != null) {
            for (int i = 1; i < n; ++i)
                if (!t.check(perm[i-1], perm[i]))
                    return 0;
        }
        int bg = 0; long res = 1;
        for (int i = 1; i < n; ++i) {
            if (c.compare(perm[bg], perm[i]) != 0) {
                res = (res * fact[i - bg]) % MOD;
                bg = i;
            }
        }
        res = (res * fact[n - bg]) % MOD;

        return res;
    }

    private static int solve(int[] a, int[] b) {
        if (a.length != b.length)
            throw new IllegalArgumentException();
        int n = a.length;

        // BAD = BAD1 or BAD2
        // #BAD = #BAD1 + #BAD2 - #(BAD1 and BAD2)
        long bad1 = cntBadBy(n, Comparator.comparingInt(i -> a[i]), null);
        long bad2 = cntBadBy(n, Comparator.comparingInt(i -> b[i]), null);
        long badBoth = cntBadBy(n, Comparator.comparingInt(i -> a[i] + b[i]), (i, j) -> a[i] <= a[j] && b[i] <= b[j]);

        return (int) ((3 * MOD + fact[n] - (bad1 + bad2 - badBoth)) % MOD);
    }

    private void run() throws Exception {
        int n = nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
            b[i] = nextInt();
        }
        println(Integer.toString(solve(a, b)));
    }

    /* ====================== Template ====================== */
    public static void main(String[] args) throws Exception {
        Main m = new Main();
        try { m.run(); } finally { m.flushWriter(); }
    }

    private final FastRead reader;
    private final FastWrite writer;

    private Main() {
        reader = new FastRead(System.in);
        writer = new FastWrite(System.out);
    }

    public String nextString(int maxLength) throws IOException { return reader.nextString(maxLength); }
    public String nextString() throws IOException { return reader.nextString(); }
    public int nextInt() throws IOException { return reader.nextInt(); }
    public long nextLong() throws IOException { return reader.nextLong(); }
    public double nextDouble() throws IOException { return reader.nextDouble(); }
    public float nextFloat() throws IOException { return reader.nextFloat(); }
    public void closeReader() throws IOException { reader.close(); }

    public void flushWriter() throws IOException { writer.flush(); }
    public void print(String s) throws IOException { writer.print(s); }
    public void println(String s) throws IOException { writer.println(s); }
    public void print(Object obj) throws IOException { writer.print(obj.toString()); }
    public void println(Object obj) throws IOException { writer.println(obj.toString()); }
    public void println() throws IOException { writer.println(); }


    static final int BUFFER_SIZE = 1<<16;
    static class FastRead {
        private final InputStream in;
        private final byte[] buffer;
        private int cur, ready;

        private void refillBuffer() throws IOException {
            ready = in.read(buffer, 0, buffer.length);
            cur = (ready == -1) ? -1 : 0;
        }

        public FastRead(InputStream in) {
            this.in = in;
            buffer = new byte[BUFFER_SIZE];
            cur = ready = 0;
        }

        private byte read() throws IOException {
            if (cur == ready) refillBuffer();
            return buffer[cur++];
        }

        public String nextString(int maxLength) throws IOException {
            byte[] res = new byte[maxLength];
            int len =  0;
            byte c = read();
            while (c == ' ' || c == '\n' || c=='\r')
                c = read();
            while (c != ' ' && c != '\n' && c!='\r') {
                res[len++] = c;
                c = read();
            }
            return new String(res, 0, len);
        }

        public String nextString() throws IOException {
            byte[] res = new byte[64];
            int len =  0;
            byte c = read();
            while (c == ' ' || c == '\n' || c=='\r')
                c = read();
            while (c != ' ' && c != '\n' && c!='\r') {
                if (len == res.length) {
                    byte[] oldRes = res;
                    res = new byte[res.length * 4];
                    System.arraycopy(oldRes, 0, res, 0, oldRes.length);
                }
                res[len++] = c;
                c = read();
            }
            return new String(res, 0, len);
        }

        public int nextInt() throws IOException {
            int ret =  0;
            boolean neg;

            byte c = read();
            while (c <= ' ')
                c = read();
            neg = c == '-';
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
                c = read();
            } while (c > ' ');

            return neg ? -ret : ret;
        }

        public long nextLong() throws IOException {
            long ret =  0;
            boolean neg;

            byte c = read();
            while (c <= ' ')
                c = read();
            neg = c == '-';
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
                c = read();
            } while (c > ' ');

            return neg ? -ret : ret;
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(nextString(32));
        }

        public float nextFloat() throws IOException {
            return Float.parseFloat(nextString(32));
        }

        public void close() throws IOException {
            in.close();
        }
    }

    static class FastWrite {
        private final OutputStream out;
        private final byte[] buffer;
        private int ready;

        public FastWrite(OutputStream out) {
            this.out = out;
            buffer = new byte[BUFFER_SIZE];
            ready = 0;
        }

        public void flush() throws IOException {
            if (ready > 0) {
                out.write(buffer, 0, ready);
                ready = 0;
            }
        }

        private void put(byte b) throws IOException {
            if (ready == buffer.length) flush();
            buffer[ready++] = b;
        }

        private void put(byte[] b) throws IOException {
            int done = 0;
            if (ready < buffer.length) {
                done = buffer.length - ready;
                if (done > b.length) done = b.length;
                System.arraycopy(b, 0, buffer, ready, done);
                ready += done;
            }

            if (ready == buffer.length) flush();
            if (done == b.length) return;
            assert ready == 0;

            if ((b.length - done) * 2 < buffer.length) {
                ready = b.length - done;
                System.arraycopy(b, done, buffer, 0, ready);
            } else {
                out.write(b, done, b.length - done);
            }
        }

        public void print(String s) throws IOException {
            put(s.getBytes());
        }

        public void println(String s) throws IOException {
            put(s.getBytes()); put((byte)'\n');
        }

        public void println() throws IOException {
            put((byte)'\n');
        }
    }
}
