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.
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		for(int q=0;q<t;q++){
		    int n = sc.nextInt();
		    int mx = -1;
		    int a[] = new int[n];
		    for(int i=0;i<n;i++){
		        a[i] = sc.nextInt();
		        mx = Math.max(mx, a[i]);
		    }
		    int cnt1=0, cnt2=0;
		    for(int i=0;i<n;i++){
		        if(a[i]==mx) cnt1++;
		        if(a[i]==mx-1) cnt2++;
		        if(cnt1>1) break;
		    }
		  //  BigInteger ans = BigIntegerMath.factorial(n);
		  //  BigInteger b = new BigInteger("998244353");
		  //  BigInteger kk = new BigInteger(Integer.toString(cnt2+1));
		  //  if(cnt1>1) {
		  //      System.out.println(ans.mod(b));
		  //  }
		  //  else{
		  //      System.out.println((ans.subtract(ans.divide(kk))).mod(b));
		  //  }
		  
		  long ans=1;
		  for(int i=2;i<=n;i++) ans = (ans*i)%998244353;
		  if(cnt1>1) System.out.println(ans);
		  else System.out.println(ans-(ans/(cnt2+1)));
		}
		
	}
}
