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. 
from sys import stdin
input = stdin.readline


mod = 998244353
MAX_N = 3*(10**5)+1
fact = [1 for i in range(MAX_N)]

for i in range(1, MAX_N):
    fact[i] = fact[i-1]*i%mod
    
n = int(input())
a = [0 for i in range(n)]
b = [0 for i in range(n)]

for i in range(n):
    a[i], b[i] = [int(i) for i in input().split()]

s = sorted([(a[i], b[i]) for i in range(n)])
a = sorted(a)
b = sorted(b)

A = 1
B = 1
S = 1

count_A = 1
count_B = 1
count_S = 1

for i in range(1, n):
    if a[i] == a[i-1]: count_A += 1
    else:
        A = (A*fact[count_A])%mod
        count_A = 1
    
    if b[i] == b[i-1]: count_B += 1
    else:
        B = (B*fact[count_B])%mod
        count_B = 1
        
    if s[i][0] == s[i-1][0]:
        if s[i][1] == s[i-1][1]: count_S += 1
        else:
            S = (S*fact[count_S])%mod
            count_S = 1
    else:
        if s[i][1] < s[i-1][1]: S = 0
        else:
            S = (S*fact[count_S])%mod
            count_S = 1
            
A = (A*fact[count_A])%mod
B = (B*fact[count_B])%mod
S = (S*fact[count_S])%mod
            
            
print(((fact[n]%mod)-A-B+S)%mod)