human
What is a Python program to print it modulo 998 244 353 given the following:
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.

class BinomialCoefficient:
    """
    Using Fermat's little theorem
    Applicable only when mod is a large prime
    """

    def __init__(self, end, _mod):
        self.end = end
        self.mod = _mod
        self.factorial = self.get_fact()

    def inv_mod(self, num):
        return pow(num, self.mod-2, self.mod)

    def get_fact(self):
        factorial = [1 for x in range(self.end)]
        for i in range(1, self.end):
            factorial[i] = factorial[i-1] * i % self.mod
        return factorial

    def binomial_coefficient(self, n, k):
        return self.factorial[n] * pow(self.factorial[k], self.mod-2, self.mod)\
               * pow(self.factorial[n-k], self.mod-2, self.mod) % self.mod

def func():
    big = max(a)
    if a.count(big) > 1:
        print(fact.factorial[n])
    else:
        k = a.count(big-1)

        if k == 0:
            print(0)
        else:
            print((fact.factorial[n] - fact.factorial[n] * fact.inv_mod(k+1)) % mod)

mod = 998_244_353
fact = BinomialCoefficient(end=2 * 10 ** 5 + 5, _mod=998_244_353)
for _ in range(int(input())):
    n = int(input())
    a = list(map(int, input().split()))
    func()