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
N = 200005
f = [1] * N
rf = [1] * N
def a(n, k):
    return f[n] * rf[n - k] % mod
def main():
    from sys import stdin
    input = stdin.buffer.readline
    for i in range(1, N):
        f[i] = f[i - 1] * i % mod
    for i in range(2, N):
        rf[i] = (mod - mod // i * rf[mod % i] % mod) % mod
    for i in range(1, N):
        rf[i] = rf[i] * rf[i - 1] % mod
    for _ in range(int(input())):
        n = int(input())
        *v, = map(int, input().split())
        mx = mx2 = 0
        cnt = cnt2 = 0
        for x in v:
            if x > mx:
                mx2 = mx
                mx = x
                cnt2 = cnt
                cnt = 1
            elif x == mx:
                cnt += 1
            elif x > mx2:
                mx2 = x
                cnt2 = 1
            elif x == mx2:
                cnt2 += 1
        if cnt > 1:
            print(f[n])
        elif mx - mx2 == 1:
            t = 0
            for i in range(cnt2, n):
                t = (t + a(i, cnt2) * f[n - cnt2 - 1] % mod) % mod
            print((f[n] - t) % mod)
        else:
            print(0)
main()
