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. 
# -*- coding:utf-8 -*-

"""

created by shuangquan.huang at 1/15/20

"""

import collections
import time
import os
import sys
import bisect
import heapq
from typing import List


MAXN = 3 * 10 ** 5 + 5
F = [1 for _ in range(MAXN)]
MOD = 998244353
for i in range(2, MAXN):
    F[i] = (i * F[i-1]) % MOD


def solve(N, A):
    va = [a for a, b in A]
    wa = collections.Counter(va)
    bada = 1
    for c in wa.values():
        bada *= F[c]
        bada %= MOD
    
    vb = [b for a, b in A]
    wb = collections.Counter(vb)
    badb = 1
    for c in wb.values():
        badb *= F[c]
        badb %= MOD
    
    badab = 0
    A.sort()
    if all([A[i][0] <= A[i+1][0] and A[i][1] <= A[i+1][1] for i in range(N-1)]):
        badab = 1
        wab = collections.Counter(A)
        for c in wab.values():
            badab *= F[c]
            badab %= MOD
            
    total = F[N]
    ans = (2 * MOD + total - bada - badb + badab) % MOD
    
    # print(total, bada, badb, badab)
    print(ans)
    

N = int(input())
A = []
for i in range(N):
    a, b = map(int, input().split())
    A.append((a, b))

solve(N, A)