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.math.*;
import java.util.*;
 
public class Main {
	//static final long MOD = 998244353;
	static final long MOD = 1000000007;
	static boolean[] visited;
    public static void main(String[] args) throws IOException {
        FastScanner sc=new FastScanner();
        int N = sc.nextInt();
        int[][] nums = new int[N][2];
        ArrayList<Integer> firsts = new ArrayList<Integer>(N);
        ArrayList<Integer> seconds = new ArrayList<Integer>(N);
        for (int i = 0; i < N; i++) {
        	firsts.add(sc.nextInt());
        	seconds.add(sc.nextInt());
        	nums[i][0] = firsts.get(i);
        	nums[i][1] = seconds.get(i);
        }
        Collections.sort(firsts);
        long firstPerms = 1;
        int first = firsts.get(0);
        int count = 0;
        for (int i = 0; i < N; i++) {
        	if (firsts.get(i) == first) {
        		count++;
        		firstPerms *= count;
        		firstPerms %= 998244353;
        	} else {
        		first = firsts.get(i);
        		count = 1;
        	}
        }
        Collections.sort(seconds);
        long secondPerms = 1;
        int second = seconds.get(0);
        count = 0;
        for (int i = 0; i < N; i++) {
        	if (seconds.get(i) == second) {
        		count++;
        		secondPerms *= count;
        		secondPerms %= 998244353;
        	} else {
        		second = seconds.get(i);
        		count = 1;
        	}
        }
        
        nums = sort(nums);
        
        long numPerms = 1;
        int[] num = nums[0];
        count = 0;
        for (int i = 0; i < N; i++) {
        	if (nums[i][0] < num[0] || nums[i][1] < num[1]) {
        		numPerms = 0;
        		break;
        	} else if (nums[i][0] == num[0] && nums[i][1] == num[1]) {
        		count++;
        		numPerms *= count;
        		numPerms %= 998244353;
        	} else {
        		num = nums[i];
        		count = 1;
        	}
        }
		
        long badPerms = firstPerms + secondPerms - numPerms;
        long ans = factorial(N) - badPerms;
        ans += 3*((long)998244353);
        ans %= 998244353;
        System.out.println(ans);
    }
    
    public static long factorial(int count) {
    	long val = 1;
    	while (count > 0) {
    		val *= count;
    		val %= 998244353;
    		count--;
    	}
    	return val;
    }

    public static int gcd(int a, int b) {
    	if (b == 0)
    		return a;
    	else
    		return gcd(b,a%b);
    }
    
    public static int[][] sort(int[][] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i < array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array, new Comparator<int[]>() {
			  @Override
        	  public int compare(int[] arr1, int[] arr2) {
	        	    if (arr1[0] != arr2[0])
	        	    	return arr1[0]-arr2[0];
	        	    else
	        	    	return arr1[1]-arr2[1];
	         }
		});
		return array;
	}
    
    static class FastScanner { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastScanner() { 
            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; 
        }
    }
}