description: n people gathered to hold a jury meeting of the upcoming competition, the i-th member of the jury came up with a_i tasks, which they want to share with each other.
  
  First, the jury decides on the order which they will follow while describing the tasks. Let that be a permutation p of numbers from 1 to n (an array of size n where each integer from 1 to n occurs exactly once).
  
  Then the discussion goes as follows:
  
    * If a jury member p_1 has some tasks left to tell, then they tell one task to others. Otherwise, they are skipped. 
    * If a jury member p_2 has some tasks left to tell, then they tell one task to others. Otherwise, they are skipped. 
    * ... 
    * If a jury member p_n has some tasks left to tell, then they tell one task to others. Otherwise, they are skipped. 
    * If there are still members with tasks left, then the process repeats from the start. Otherwise, the discussion ends. 
  
  
  
  A permutation p is nice if none of the jury members tell two or more of their own tasks in a row. 
  
  Count the number of nice permutations. The answer may be really large, so print it modulo 998 244 353.
  
  Input
  
  The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.
  
  The first line of the test case contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — number of jury members.
  
  The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the number of problems that the i-th member of the jury came up with.
  
  The sum of n over all test cases does not exceed 2 ⋅ 10^5.
  
  Output
  
  For each test case, print one integer — the number of nice permutations, taken modulo 998 244 353.
  
  Example
  
  Input
  
  
  4
  2
  1 2
  3
  5 5 5
  4
  1 3 3 7
  6
  3 4 2 1 3 3
  
  
  Output
  
  
  1
  6
  0
  540
  
  Note
  
  Explanation of the first test case from the example:
  
  There are two possible permutations, p = [1, 2] and p = [2, 1]. For p = [1, 2], the process is the following:
  
    1. the first jury member tells a task; 
    2. the second jury member tells a task; 
    3. the first jury member doesn't have any tasks left to tell, so they are skipped; 
    4. the second jury member tells a task. 
  
  
  
  So, the second jury member has told two tasks in a row (in succession), so the permutation is not nice.
  
  For p = [2, 1], the process is the following:
  
    1. the second jury member tells a task; 
    2. the first jury member tells a task; 
    3. the second jury member tells a task. 
  
  
  
  So, this permutation is nice.
solution: #include <bits/stdc++.h>
  using namespace std;
  long long mod = 998244353;
  long long f(int n) {
    long long q = 1;
    for (int i = 1; i <= n; i++) {
      q %= mod;
      q = (q * i) % mod;
      q % mod;
    }
    return q;
  }
  long long d(int n, int x) {
    long long s = 1;
    for (int i = 1; i <= n; i++) {
      if (i != x + 1) {
        s %= mod;
        s = (s * i) % mod;
        s %= mod;
      }
    }
    s = s * (x) % mod;
    s %= mod;
    return s;
  }
  int main() {
    int t;
    cin >> t;
    while (t--) {
      int n;
      long long ans = 0, g = 0, j = 0;
      cin >> n;
      int a[n];
      long long mx = INT_MIN;
      for (int i = 0; i < n; i++) {
        long long x;
        cin >> x;
        mx = max(mx, x);
        a[i] = x;
      }
      for (int i = 0; i < n; i++) {
        if (a[i] == mx - 1) {
          g++;
        }
        if (a[i] == mx) {
          j++;
        }
      }
      if (j >= 2) {
        ans = f(n);
        ans %= mod;
      } else {
        if (g != 0) {
          ans = d(n, g);
        }
      }
      cout << ans << "\n";
    }
  }
  