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.
mod=998244353

def power(x,y,p):
    res=1
    x=x%p
    while y>0:
        if y&1:
            res = (res * x) % p
        y=y>>1
        x=(x*x)%p
    return res

def modinv(n,p):
    return power(n,p-2,p)

def ncr(n,r,p):
    if n<r:
        return 0
    if r==0:
        return 1
    return (fac[n]*modinv(fac[r],p)%p*modinv(fac[n-r],p)%p)%p

def fun():
    n=int(input())
    a=list(map(int,input().split()))
    a=sorted(a)
    if a[n-1]-a[n-2]>1:
        print(0)
        return
    if n==1:
        print(1)
    elif a[n-1]==a[n-2]:
        print(fac[n])
    else:
        nu=0
        for i in range(n):
            if a[i]<a[n-2]:
                nu+=1
        ans=fac[n]
        to=0
        for i in range(nu+1):
            xo= (fac[n-i-1]*ncr(nu,i,mod))%mod
            xo= (xo*fac[i])%mod
            to= (to + xo)%mod
        print((ans-to+mod)%mod)

fac=[0]*200007
fac[0]=1
for i in range(1,200007):
    fac[i]=(fac[i-1]*i)%mod
for _ in range(int(input())):
    fun()
    
