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. 
import sys
def main():
    input = sys.stdin.readline
    n = int(input())
    dg = 10**9
    mod = 998244353

    f = [1]
    for i in range(1,n+10):
        f.append(f[-1]*i%mod)

    p = []
    q = []
    r = []

    for _ in [0]*n:
        x,y = map(int,input().split())
        p.append(x)
        q.append(y)
        r.append(x*dg+y)

    p.sort()
    q.sort()
    r.sort()

    a = 1
    cnt = 1
    for i in range(1,n):
        if p[i] == p[i-1]:
            cnt += 1
        else:
            a = a*f[cnt]%mod
            cnt = 1
    a = a*f[cnt]%mod

    b = 1
    cnt = 1
    for i in range(1,n):
        if q[i] == q[i-1]:
            cnt += 1
        else:
            b = b*f[cnt]%mod
            cnt = 1
    b = b*f[cnt]%mod

    judge = True
    for i in range(n):
        if q[i] != r[i]%dg:
            judge = False
    
    if not judge:
        print((f[n]-a-b)%mod)
        return
    
    c = 1
    cnt = 1
    for i in range(1,n):
        if r[i] == r[i-1]:
            cnt += 1
        else:
            c = c*f[cnt]%mod
            cnt = 1
    c = c*f[cnt]%mod
    print((f[n]-a-b+c)%mod)


if __name__ == '__main__':
    main()