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 int m = 998244353, f[300001];
void fact() {
  f[1] = 1;
  for (long long int i = 2; i <= 300000; i++) {
    f[i] = f[i - 1] * i;
    f[i] = f[i] % m;
  }
}
bool comp(pair<long long int, long long int> p,
          pair<long long int, long long int> q) {
  return p.second < q.second;
}
int main() {
  long long int ans = 0, ans2 = 1;
  long int long n;
  cin >> n;
  fact();
  ans += f[n];
  ans %= m;
  vector<pair<long long int, long long int>> v;
  for (long long int i = 0; i < n; i++) {
    long long int a, b;
    cin >> a >> b;
    v.push_back(make_pair(a, b));
  }
  sort(v.begin(), v.end(), comp);
  for (long long int i = 0; i < v.size(); i++) {
    long long int c = 0, temp = v[i].second;
    while (v[i].second == temp) {
      i++;
      c++;
    }
    i--;
    ans2 *= f[c];
    ans2 %= m;
  }
  ans -= ans2;
  ans += m;
  ans %= m;
  ans2 = 1;
  sort(v.begin(), v.end());
  for (long long int i = 0; i < v.size(); i++) {
    long long int c = 0, temp = v[i].first;
    while (v[i].first == temp) {
      i++;
      c++;
    }
    i--;
    ans2 *= f[c];
    ans2 %= m;
  }
  ans -= ans2;
  ans += m;
  ans %= m;
  int c = 1;
  for (long long int i = 1; i < v.size(); i++) {
    if (v[i].second < v[i - 1].second) c = 0;
  }
  if (c == 1) {
    ans2 = 1;
    for (long long int i = 0; i < v.size(); i++) {
      long long int temp = v[i].first;
      while (v[i].first == temp) {
        long long int c = 0, temp2 = v[i].second;
        while (v[i].second == temp2 && v[i].first == temp) {
          i++;
          c++;
        }
        ans2 *= f[c];
        ans2 %= m;
      }
      i--;
    }
    ans += ans2;
    ans %= m;
  }
  cout << ans;
}
