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.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.InputMismatchException;
public class DEducation71B {
	
	public static final long p = 998244353L;
	public static long[] fact;
	
	public static void main(String[] args) {
		FastScanner in = new FastScanner(System.in);
		int N = in.nextInt();
		
		fact = new long[N+1];
		fact[0] = 1;
		for(int i = 1; i < fact.length; i++) {
			fact[i] = (fact[i-1] * i) % p;
		}
		
		ArrayList<Integer> a = new ArrayList<>();
		ArrayList<Integer> b = new ArrayList<>();
		ArrayList<Pair> c = new ArrayList<>();
		
		for(int i = 0; i < N; i++) {
			int x = in.nextInt();
			int y = in.nextInt();
			a.add(x);
			b.add(y);
			c.add(new Pair(x, y));
		}
		
		HashMap<Integer, Integer> mapA = new HashMap<>();
		HashMap<Integer, Integer> mapB = new HashMap<>();
		HashMap<Pair, Integer> mapC = new HashMap<>();
		
		for(int i : a) {
			if(!mapA.containsKey(i)) {
				mapA.put(i, 1);
			}
			else {
				mapA.put(i, mapA.get(i) + 1);
			}
		}
		
		for(int i : b) {
			if(!mapB.containsKey(i)) {
				mapB.put(i, 1);
			}
			else {
				mapB.put(i, mapB.get(i) + 1);
			}
		}
		
		for(Pair pair : c) {
			if(!mapC.containsKey(pair)) {
				mapC.put(pair, 1);
			}
			else {
				mapC.put(pair, mapC.get(pair) + 1);
			}
		}
		
		Collections.sort(c);
		
		long prod0 = 1;
		long prod1 = 1;
		long prod2 = 1;
		
		for(int i : mapA.keySet()) {
			int val = mapA.get(i);
			prod0 = (prod0 * fact[val]) % p;
		}
		
		for(int i : mapB.keySet()) {
			int val = mapB.get(i);
			prod1 = (prod1 * fact[val]) % p;
		}
		
		for(Pair pair : mapC.keySet()) {
			int val = mapC.get(pair);
			prod2 = (prod2 * fact[val]) % p;
		}
		
		for(int i = 1; i < c.size(); i++) {
			if(c.get(i-1).b > c.get(i).b) {
				prod2 = 0;
				break;
			}
		}
		
	//	System.out.println("prod0, prod1, prod2 = " + prod0 + " " + prod1 + " " + prod2);
		
		long subtract = (((prod0 + prod1) % p) + p - prod2) % p;
		long result = (fact[N] - subtract) % p;
		if(result < 0) {
			result += p;
		}
		
		System.out.println(result);
	}
	
	public static class Pair implements Comparable<Pair> {
		int a, b;
		public Pair(int x, int y) {
			a = x;
			b = y;
		}
		
		public int compareTo(Pair p2) {
			if(a == p2.a) {
				return b - p2.b;
			}
			return a - p2.a;
		}
		
		public boolean equals(Object o) {
			if(!(o instanceof Pair)) {
				return false;
			}
			
			Pair p2 = (Pair) o;
			return a == p2.a && b == p2.b;
		}
		
		public int hashCode() {
			return (a + " " + b).hashCode();
		}
	}
	
	/**
	 * Source: Matt Fontaine
	 */
	static class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int chars;

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

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

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

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

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

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

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

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

		public String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}
	
}
/*
3
1 1
2 2
3 1
outputCopy
3
inputCopy
4
2 3
2 2
2 1
2 4
outputCopy
0
inputCopy
3
1 1
1 1
2 3
outputCopy
4
*/