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;
const long long MAXN = 3 * 1e5 + 100;
long long n, f[MAXN], ans, t[MAXN];
long long m;
struct node {
  long long a, b;
} sh[MAXN];
bool cmp(node a, node b) { return (a.a < b.a || (a.a == b.a && a.b < b.b)); }
int main() {
  scanf("%lld", &n);
  for (long long i = 1; i <= n; i++) scanf("%lld%lld", &sh[i].a, &sh[i].b);
  f[1] = 1;
  for (long long i = 2; i <= n; i++) f[i] = (f[i - 1] * i) % 998244353;
  ans = f[n];
  for (long long i = 1; i <= n; i++) t[sh[i].a]++;
  m = 1;
  for (long long i = 1; i <= n; i++) {
    if (t[i] > 1) m = (m * f[t[i]]) % 998244353;
  }
  ans = (ans - m + 998244353) % 998244353;
  memset(t, 0, sizeof(t));
  for (long long i = 1; i <= n; i++) t[sh[i].b]++;
  m = 1;
  for (long long i = 1; i <= n; i++) {
    if (t[i] > 1) m = (m * f[t[i]]) % 998244353;
  }
  ans = (ans - m + 998244353) % 998244353;
  sort(sh + 1, sh + 1 + n, cmp);
  bool bl = 1;
  for (long long i = 2; i <= n; i++) {
    if (sh[i].b < sh[i - 1].b) {
      bl = 0;
      break;
    }
  }
  if (!bl) {
    printf("%lld\n", ans);
    return 0;
  }
  node kind;
  long long w = 1;
  kind = sh[1];
  m = 1;
  for (long long i = 2; i <= n; i++) {
    if (sh[i].a == kind.a && sh[i].b == kind.b)
      w++;
    else {
      m = (m * f[w]) % 998244353;
      w = 1;
      kind = sh[i];
    }
  }
  m = (m * f[w]) % 998244353;
  ans = (ans + m) % 998244353;
  printf("%lld\n", ans);
}
