human
Write me a Python code to print it modulo 998 244 353 given the following:
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 code to print it modulo 998 244 353.
 def f(n):
    res = 1
    for i in range(2, n + 1):
        res = res * i % 998244353
    return res

def g(a, b):
    res = 1
    for i in range(2, a + b + 1):
        if i != b:
            res = res * i % 998244353
    res = res * (b - 1) % 998244353
    return res

for t in range(int(input())):
    n = int(input())
    s = list(map(int, input().split()))
    mx = max(s)
    if n == 1:
        print(1 if mx <= 1 else 0)
    if s.count(mx) == 1:
        smx = [0, 0]
        for i in s:
            if i != mx:
                if i == smx[0]:
                    smx[1] += 1
                else:
                    smx = max(smx, [i, 1])
        if smx[0] == mx - 1:
            print(g(n - smx[1] - 1, smx[1] + 1))
        else:
            print(0)
    else:
        print(f(n))