human
PYTHON3 solution for "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;...":
assistant
#Here is Python program to print it modulo 998 244 353.
 def main():
    # mod=1000000007 
    # MOD THE ANSWER IF USING THIS
    mod=998244353
    max_n=200005
    nCr,fact =  make_nCr_mod(max_n,mod)
    
    tc=ri()
    for i in range(tc): 
        n=ri()
        a=ria()
        a=sorted(a)
        cnt=Counter(a)
        if a[-1]-a[-2]>=2:
            wi(0)
            continue
        if cnt[a[-1]]>=2:
            wi(fact[n])
        else:     
            k=cnt[a[-1]-1]
            # only thing that matters is subsequence which has a[-1] and k a[-1]-1
            # let a[-1] be p and a[-1]-1 be q
            # p can take any place in the subsequence except last position
            # length of subsequence is k+1 and p can take first k positions so atleast 1 q comes after p
            # ans = (total permutations) *(k/(k+1))
            wi((k*fact[n]*pow(k+1,mod-2,mod))%mod)

        
def rant():
    # RANT BEGINS-
    # 
    # Did you look at the constraints dummy? Read problem again carefully understand it correctly
    # Are base cases correct n=0,n=1,n=N or string is all 0 or all 1?
    # Take hints from time limits maybe n=1000 and m=100000 so if n^2 doesnt work n*m might work?? 
    # Upto 10^8 works under 2 sec
    # 
    # 1.Greedy? What matters what doesnt? Is my claim correct? 
    #   Does my implementation correctly implements the greedy i thought of? 
    #   Dictionary? keep a count of values if constraint on something is low(like only alphabets(26) count)? 
    # 
    # 2.DP? Think about state's ranges maybe one of the states have lesser possible values than it may look like? 
    #   Obviously think about order of evaluation?
    #   Max/Min Answer including ith element or Ways to Answer using first i elements?
    # 
    # 3.Binary Search?(Monotonic? any one directed order in which we have to perform something?)
    # 
    # 4.Graph?DSU?Edge property or Vertex property Read carefully? Bipartitenes Property??? Cycle Property??? 
    #   Hidden but dependency ordering of values(in 1d array or 2d Table/Array) is that of a graph???
    # 
    #...