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. 
# TAIWAN NUMBER ONE!!!!!!!!!!!!!!!!!!!
# TAIWAN NUMBER ONE!!!!!!!!!!!!!!!!!!!
# TAIWAN NUMBER ONE!!!!!!!!!!!!!!!!!!!
from sys import stdin, stdout
from collections import defaultdict
import math
import copy
 
#T = int(input())
N = int(input())
#s = input()
#N,M = [int(x) for x in stdin.readline().split()]
#arr = [int(x) for x in stdin.readline().split()]
 
permu = [0]*N
permu[0] = 1
for i in range(1,N):
    permu[i] = (permu[i-1]*(i+1))%998244353

data = []
pair = {}
for i in range(N):
    a,b = [int(x) for x in stdin.readline().split()]
    data.append((a,b))
    if a not in pair:
        pair[a] = []
        
    pair[a].append(b)
    
    
freq_one = {}
for i in range(N):
    a = data[i][0]
    if a not in freq_one:
        freq_one[a] = 1
    else:
        freq_one[a] += 1
        
all = permu[-1]

# first column
p1 = 1
for key in freq_one:
    f = freq_one[key]
    p1 *= permu[f-1]
    p1 = p1%998244353

freq_two = {}
for i in range(N):
    a = data[i][1]
    if a not in freq_two:
        freq_two[a] = 1
    else:
        freq_two[a] += 1
        
# second column        
p2 = 1
for key in freq_two:
    f = freq_two[key]
    p2 *= permu[f-1]
    p2 = p2%998244353
    
# both sorted
max_second = 0
P = list(pair.keys())
P.sort()

p3 = 1
for key in P:
    #print(key)
    mini = min(pair[key])
    if mini<max_second:
        p3 = 0
        break
    
    f = {}
    for a in pair[key]:
        if a not in f:
            f[a] = 1
        else:
            f[a] += 1
            
    p = 1
    for num in f:
        fr = f[num]
        p *= permu[fr-1]
        p = p%998244353
        
    p3 *= p
    p3 = p3%998244353
    
    max_second = max(pair[key])
    
ans = (all-p1-p2+p3)%998244353

print(ans)


    

    