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. 
'''input
3
1 1
2 2
3 1

'''
import sys
from collections import defaultdict as dd
mod=998244353  

def ri(flag=0):
	if flag==0:
		return [int(i) for i in sys.stdin.readline().split()]
	else:
		return int(sys.stdin.readline())


n = ri(1)

one = []
sec = []
take = []
for i in range(n):
	a, b = ri()
	one.append(a)
	sec.append(b)
	take.append((a,b))

ans = 1
temp =1

for i in range(1,n+1):
	ans = (ans*i)%mod

take.sort()

# good good
cnt1=0
cnt2=0
# check = [[0,0] for i in range(n)]

# for i in range(1,n):
# 	if take[i][0] != take[i-1][0]:
# 		check[i][0] = check[i-1][0]+1
# 	else:
# 		check[i][0] = check[i-1][0]

# 	if take[i][1] != take[i-1][1]:
# 		check[i][1] = check[i-1][1]+1
# 	else:
# 		check[i][1] = check[i-1][1]

c1= dd(int)
c2 = dd(int)
c3 =dd(int)


status=1

for i in range(1,n):
	if take[i][1]<take[i-1][1]:
		status=0

for i in one:
	c1[i]+=1
for i in sec:
	c2[i]+=1
for i in take:
	c3[i]+=1

ok1=1
ok2=1
ok3=1

#print(c1,c2,c3)

fac= [1 for i in range(3*10**5+1)]

for i in range(1,3*10**5+1):
	fac[i] = (fac[i-1]*i)%mod

for i in c1:
	ok1 = (ok1*fac[c1[i]])%mod

for i in c2:
	ok2 = (ok2*fac[c2[i]])%mod

for i in c3:
	ok3 = (ok3*fac[c3[i]])%mod

if status==0:
	ok3 = 0

print( (ans - ok1 - ok2 +ok3)%mod)
