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
n = int(input())
p = 998244353
sil = [0] * 400000
sil[1] = 1
for i in range(2, 400000):
    sil[i] = (sil[i -1] * i) % p
def fun(l):
    wyn = 1
    l.sort()
    count = 1
    for i in range(1, len(l)):
        if l[i] != l[i-1]:
            wyn = (wyn * sil[count]) % p
            count = 1
        else:
            count += 1
    wyn = (wyn * sil[count]) % p
    return wyn
dupa = [list(map(int,input().split())) for i in range(n)]
xx = [i[0] for i in dupa]
yy = [i[1] for i in dupa]
dupa.sort()
x = [i[0] for i in dupa]
y = [i[1] for i in dupa]
dolne = []
pyk = 1
left = 0
for i in range(1, n):
    if x[i] != x[i-1]:
        dolne.append(y[left:i])
        left = i
if left == n - 1:
    dolne.append([y[n - 1]])
else:
    dolne.append(y[left:n])
c = 1
for i in range(1, len(dolne)):
    if min(dolne[i]) < max(dolne[i - 1]):
        c = 0
        break
# c = 0 means no overlaps

wyn = fun(xx) + fun(yy)
if c == 1:
    dupa = 1
    for i in range(len(dolne)):
        dupa = (dupa * fun(dolne[i])) % p
    wyn -= dupa
print((sil[n] - wyn) % p)