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;
namespace wode {
template <typename T>
inline void read(T &x) {
  static char ch;
  bool f = 1;
  for (x = 0, ch = getchar(); !isdigit(ch); ch = getchar())
    if (ch == '-') f = 0;
  for (; isdigit(ch); x = (x << 1) + (x << 3) + (ch ^ 48), ch = getchar())
    ;
  x = f ? x : -x;
}
template <typename T>
void print(T x) {
  if (x < 0) putchar('-'), x = -x;
  if (x >= 10) print(x / 10);
  putchar(x % 10 + '0');
}
template <typename T>
inline void print(T x, char ap) {
  print(x);
  if (ap) putchar(ap);
}
template <typename T>
inline T max(T x, T y) {
  return x < y ? y : x;
}
template <typename T>
inline T min(T x, T y) {
  return x < y ? x : y;
}
template <typename T>
inline void chkmax(T &x, T y) {
  x = x < y ? y : x;
}
template <typename T>
inline void chkmin(T &x, T y) {
  x = x < y ? x : y;
}
}  // namespace wode
using wode::chkmax;
using wode::chkmin;
using wode::print;
using wode::read;
const int mod = 998244353;
struct node {
  int x, y;
  bool operator<(const node &b) const {
    return x < b.x || (x == b.x && y < b.y);
  }
} a[300010];
int n, sum, fac[300010];
inline bool cmp1(const node &a, const node &b) { return a.x < b.x; }
inline bool cmp2(const node &a, const node &b) { return a.y < b.y; }
int main() {
  read(n), fac[0] = 1;
  for (register int i = 1; i <= n; ++i)
    fac[i] = (long long)fac[i - 1] * i % mod;
  for (register int i = 1; i <= n; ++i) read(a[i].x), read(a[i].y);
  a[n + 1].x = 1e9, a[n + 1].y = 1e9;
  sort(a + 1, a + 1 + n, cmp1);
  int tot = 1, ans = 1;
  for (register int i = 2; i <= n + 1; ++i)
    if (a[i].x == a[i - 1].x)
      ++tot;
    else
      ans = (long long)ans * fac[tot] % mod, tot = 1;
  sum += ans, sum = sum >= mod ? sum - mod : sum;
  sort(a + 1, a + 1 + n, cmp2);
  tot = 1, ans = 1;
  for (register int i = 2; i <= n + 1; ++i)
    if (a[i].y == a[i - 1].y)
      ++tot;
    else
      ans = (long long)ans * fac[tot] % mod, tot = 1;
  sum += ans, sum = sum >= mod ? sum - mod : sum;
  sort(a + 1, a + 1 + n);
  tot = 1, ans = 1;
  for (register int i = 2; i <= n; ++i)
    if (a[i].y < a[i - 1].y) return print((fac[n] - sum + mod) % mod, '\n'), 0;
  for (register int i = 2; i <= n + 1; ++i)
    if (a[i].y == a[i - 1].y && a[i].x == a[i - 1].x)
      ++tot;
    else
      ans = (long long)ans * fac[tot] % mod, tot = 1;
  sum -= ans, sum = sum < 0 ? sum + mod : sum;
  print((fac[n] - sum + mod) % mod, '\n');
  return 0;
}
