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 int maxn = 3e5 + 5;
const long long mod = 998244353;
long long jc[maxn];
struct node {
  int l, r;
} a[maxn];
bool cmp1(node a, node b) {
  if (a.l != b.l) return a.l < b.l;
  return a.r < b.r;
}
bool cmp2(node a, node b) {
  if (a.r != b.r) return a.r < b.r;
  return a.l < b.l;
}
int main() {
  jc[0] = 1;
  for (int i = (1); i <= (300000); i++) jc[i] = (jc[i - 1] * i) % mod;
  int n;
  scanf("%d", &n);
  for (int i = (1); i <= (n); i++) scanf("%d", &a[i].l), scanf("%d", &a[i].r);
  sort(a + 1, a + n + 1, cmp1);
  long long ans1 = 1;
  int p1 = 1;
  for (int i = (1); i <= (n + 1); i++) {
    if (a[p1].l != a[i].l) {
      ans1 = (ans1 * jc[i - p1]) % mod;
      p1 = i;
    }
  }
  sort(a + 1, a + n + 1, cmp2);
  p1 = 1;
  long long ans2 = 1;
  for (int i = (1); i <= (n + 1); i++) {
    if (a[p1].r != a[i].r) {
      ans2 = (ans2 * jc[i - p1]) % mod;
      p1 = i;
    }
  }
  bool flag = 1;
  for (int i = (1); i <= (n); i++)
    if (a[i].l < a[i - 1].l || a[i].r < a[i - 1].r) {
      flag = 0;
      break;
    }
  long long ans = (ans1 + ans2) % mod;
  if (flag) {
    p1 = 1;
    long long res = 1;
    for (int i = (1); i <= (n + 1); i++) {
      if (a[p1].l != a[i].l || a[p1].r != a[i].r) {
        res = (res * jc[i - p1]) % mod;
        p1 = i;
      }
    }
    ans = ((ans - res) % mod + mod) % mod;
  }
  ans = ((jc[n] - ans) % mod + mod) % mod;
  cout << ans;
}
