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. 
# https://codeforces.com/contest/1207/problem/D
from sys import stdin
n   = int(input())
p   = [list(map(int, stdin.readline().split())) for _ in range(n)]
mod = 998244353  
da  = {}
db  = {}

def normal(x):
    while x < mod:
        x += mod
    return x % mod    
    
gt  = [1] * (n+1)
for i in range(1, n+1):
    gt[i] = gt[i-1] * i % mod
    
for i, [a,b] in enumerate(p):
    if a not in da:
        da[a] = []
    da[a].append(b)

    if b not in db:
        db[b] = 0
    db[b] += 1

ans  = 0
temp = 1
for v in da.values():
    temp = temp * gt[len(v)] % mod
ans += temp    

temp = 1
for v in db.values():
    temp = temp * gt[v] % mod

ans = (ans + temp)  % mod   

pre_max = 0
minus   = 1
for k, v in sorted(da.items(), key=lambda x:x[0]):
    d = {}
    min_ = n+1
    max_ = 0
    
    for b in v:
        if b < min_:
            min_ = b
        if b > max_:
            max_ = b
        
        if b not in d:
            d[b] = 0
        d[b] += 1
    
    if min_ < pre_max:
        minus = 0
        break
        
    pre_max = max_    
    
    for v in d.values():
        minus = minus * gt[v] % mod
        
ans -= minus
print(normal(gt[n] - ans))

#4
#2 3
#2 2
#2 1
#2 4