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. 
#include <bits/stdc++.h>
using namespace std;
long long s1, s2, s3, s4;
int n;
struct mzls {
  int x, y;
  bool operator<(const mzls &a1) const {
    return x == a1.x ? y < a1.y : x < a1.x;
  }
} a[1000005];
map<int, map<int, int> > mp;
int t1[1000005], t2[1000005];
int main() {
  s1 = s2 = s3 = s4 = 1;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d%d", &a[i].x, &a[i].y);
    mp[a[i].x][a[i].y]++;
    t1[a[i].x]++, t2[a[i].y]++;
    s3 = s3 * t1[a[i].x] % 998244353;
    s4 = s4 * t2[a[i].y] % 998244353;
    s1 = s1 * mp[a[i].x][a[i].y] % 998244353;
    s2 = s2 * i % 998244353;
  }
  sort(a + 1, a + n + 1);
  bool f1 = 0;
  for (int i = 1; i < n; i++)
    if (a[i].x > a[i + 1].x || a[i].y > a[i + 1].y) f1 = 1;
  s2 = ((s2 - s3 + 998244353) % 998244353 - s4 + 998244353) % 998244353;
  if (!f1) s2 = (s2 + s1) % 998244353;
  printf("%lld", s2);
  return 0;
}
