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.
import sys,math
from collections import deque,defaultdict
import operator as op
from functools import reduce
from itertools import permutations
import heapq

#sys.setrecursionlimit(10**7) 
# OneDrive\Documents\codeforces

I=sys.stdin.readline

alpha="abcdefghijklmnopqrstuvwxyz"

mod=10**9 + 7

"""
x_move=[-1,0,1,0,-1,1,1,-1]
y_move=[0,1,0,-1,1,1,-1,-1]
"""
def ii():
	return int(I().strip())
def li():
	return list(map(int,I().strip().split()))
def mi():
	return map(int,I().strip().split())


def ncr(n, r):
    r = min(r, n-r)
    numer = reduce(op.mul, range(n, n-r, -1), 1)
    denom = reduce(op.mul, range(1, r+1), 1)
    return numer // denom 

def mod_ncr(n, r, p):
    return (fact[n] * pow(fact[r]*fact[n-r],p - 2, p)) % p

def ispali(s):
	i=0
	j=len(s)-1

	while i<j:
		if s[i]!=s[j]:
			return False
		i+=1
		j-=1
	return True



def isPrime(n):
	if n<=1:
		return False
	elif n<=2:
		return True
	else:
		
		for i in range(2,int(n**.5)+1):
			if n%i==0:
				return False
		return True
mod=998244353
fact=[1]*(3*10**5)
for i in range(2,3*10**5):
	fact[i]=(fact[i-1]*i)%mod


def main():
	ans=""
	
	for _ in range(ii()):
		n=ii()
		arr=sorted(li())
		mx=arr[-1]

		if arr.count(mx)>1:
			ans+=str(fact[n])+"\n"
		else:
			mx2=arr[-2]
			if mx-mx2>1:
				ans+="0\n"
			else:
				x=fact[n]
				cnt_mx2=arr.count(mx2)
				tmp=0
				for i in range(n-1,cnt_mx2-1,-1):
					tmp+=(mod_ncr(i,cnt_mx2,mod))%mod
				# print(tmp)
				tmp%=mod

				tmp=(fact[n-cnt_mx2-1]*fact[cnt_mx2]*tmp)%mod
				ans+=str((x-tmp)%mod)+"\n"
	print(ans)


		
		
	




		
	
	
			

	


	













		

		


		









		



		







	

	


	
	

	




	


 
		





	

	


			









	


				


	

	
	

	




	


	




		
	












































					

if __name__ == '__main__':
	main()