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;...":



Can you provide a Python program to print it modulo 998 244 353?
assistant
#Here is Python program to print it modulo 998 244 353.
 def sol():
    n = int(input())
    arr = [int(x) for x in input().split()]
    m = 998244353
    fact = (n+1)*[0]
    fact[0] = 1
    for i in range(1,n+1):
        fact[i] = (fact[i-1]*i)%m
    if n == 1:
        return 1
    cnt = dict()
    maksi = 0
    for el in arr:
        cnt[el] = cnt.get(el, 0) + 1
        maksi = max(maksi, el)
    if cnt[maksi] != 1:
        return fact[n]
    if (maksi - 1) not in cnt:
        return 0
    rozne = cnt[maksi-1]
    inne = n - 1 - rozne
    lewa = 1
    ans = 0
    for i in range(n,rozne,-1):
        ans = (ans + fact[rozne+inne] * lewa) % m
        lewa = (lewa * inne) % m
        inne -= 1
    return (fact[n] - ans)%m

def main():
    for i in range(int(input())):
        print(sol())

main()