B'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: 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)] . The first line contains one integer n ( 1 <= n <= 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 <= a_i, b_i <= n ) -- the first and second elements of i -th pair in the sequence. The sequence s may contain equal elements. 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). In first test case there are six permutations of size 3 : '...