D. Number Of Permutationstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a sequence of n pairs of integers: (a_1, b_1), (a_2, b_2), \dots , (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, \dots , p_n consisting of n distinct integers from 1 to n (1 \le p_i \le n). If you apply permutation p_1, p_2, \dots , p_n to the sequence s_1, s_2, \dots , s_n you get the sequence s_{p_1}, s_{p_2}, \dots , 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)].InputThe first line contains one integer n (1 \le n \le 3 \cdot 10^5).The next n lines contains description of sequence s. The i-th line contains two integers a_i and b_i (1 \le a_i, b_i \le n) — the first and second elements of i-th pair in the sequence.The sequence s may contain equal elements.OutputPrint 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).ExamplesInput
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
NoteIn first test case there are six permutations of size 3:   if p = [1, 2, 3], then s = [(1, 1), (2, 2), (3, 1)] — bad sequence (sorted by first elements);  if p = [1, 3, 2], then s = [(1, 1), (3, 1), (2, 2)] — bad sequence (sorted by second elements);  if p = [2, 1, 3], then s = [(2, 2), (1, 1), (3, 1)] — good sequence;  if p = [2, 3, 1], then s = [(2, 2), (3, 1), (1, 1)] — good sequence;  if p = [3, 1, 2], then s = [(3, 1), (1, 1), (2, 2)] — bad sequence (sorted by second elements);  if p = [3, 2, 1], then s = [(3, 1), (2, 2), (1, 1)] — good sequence. 
3
1 1
2 2
3 1

3 
['combinatorics', '*1800']