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 D implements Runnable {
	public static void main (String[] args) {new Thread(null, new D(), "_cf", 1 << 28).start();}

	public void run() {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		System.err.println("");

		int n = fs.nextInt();
		int[] fact = new int[n+1];
		fact[0] = 1;
		for(int i = 1; i <= n; i++) fact[i] = mult(fact[i-1], i);
		
		Pair[] a = new Pair[n];
		for(int i = 0; i < n; i++) {
			a[i] = new Pair(fs.nextInt(), fs.nextInt(), i);
		}
		Arrays.sort(a, new Comp1());
		int b1 = 1;
		for(int i = 0; i < n; i++) {
			int j = i;
			while(j < n && a[i].x == a[j].x) j++;
			b1 = mult(b1, fact[j-i]);
			i = --j;
		}
		
		Arrays.sort(a, new Comp2());
		int b2 = 1;
		for(int i = 0; i < n; i++) {
			int j = i;
			while(j < n && a[i].y == a[j].y) j++;
			b2 = mult(b2, fact[j-i]);
			i = --j;
		}
		
		Arrays.sort(a, new Comp3());
		int b3 = 1;
		for(int i = 0; i < n-1; i++) {
			if(a[i].x <= a[i+1].x && a[i].y <= a[i+1].y) {
				
			}
			else {
				b3 = 0;
			}
		}
		
		for(int i = 0; i < n; i++) {
			int j = i;
			while(j < n && a[j].x == a[i].x && a[j].y == a[i].y) j++;
			b3 = mult(b3, fact[j-i]);
			i = --j;
		}
		
		int res = add(b1, b2);
		res = sub(res, b3);
		out.println(sub(fact[n], res));
		
		out.close();
	}
	
	int MOD = 998244353;
	
	int sub(int a, int b) {
		a -= b;
		if(a < 0) a += MOD;
		return a;
	}
	
	int add(int a, int b) {
		a += b;
		if(a >= MOD) a -= MOD;
		return a;
	}
	
	int mult(long a, long b) {
		a *= b;
		if(a >= MOD) a %= MOD;
		return (int)a;
	}
	
	class Pair {
		int x, y, id;
		int min, max;
		Pair(int a, int b, int i) {
			x = a; y = b;
			min = Math.min(x, y);
			max = Math.max(x, y);
			id = i;
		}
	}
	
	class Comp1 implements Comparator<Pair> {
		public int compare(Pair a, Pair b) {
			return Integer.compare(a.x, b.x);
		}
	}
	
	class Comp2 implements Comparator<Pair> {
		public int compare(Pair a, Pair b) {
			return Integer.compare(a.y, b.y);
		}
	}
	
	class Comp3 implements Comparator<Pair> {
		public int compare(Pair a, Pair b) {
			int c = Integer.compare(a.min, b.min);
			if(c == 0) c = Integer.compare(a.max, b.max);
			return c;
		}
	}
	

	class FastScanner {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public FastScanner() {
			in = new BufferedInputStream(System.in, BS);
		}

		public FastScanner(String s) {
			try {
				in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
			}
			catch (Exception e) {
				in = new BufferedInputStream(System.in, BS);
			}
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}                
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
		
		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for(int i = 0; i < n; i++) res[i] = nextInt();
			return res;
		}
		
	}

}