# For Solution

nn people gathered to hold a jury meeting of the upcoming competition, the ii-th member of the jury came up with aiai 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 pp of numbers from 11 to nn (an array of size nn where each integer from 11 to nn occurs exactly once).

Then the discussion goes as follows:

• If a jury member p1p1 has some tasks left to tell, then they tell one task to others. Otherwise, they are skipped.
• If a jury member p2p2 has some tasks left to tell, then they tell one task to others. Otherwise, they are skipped.
• If a jury member pnpn 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 pp 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 998244353998244353.

## Jury Meeting solution codeforces

The first line contains a single integer tt (1t1041≤t≤104) — the number of test cases.

The first line of the test case contains a single integer nn (2n21052≤n≤2⋅105) — number of jury members.

The second line contains nn integers a1,a2,,ana1,a2,…,an (1ai1091≤ai≤109) — the number of problems that the ii-th member of the jury came up with.

The sum of nn over all test cases does not exceed 21052⋅105.

## Jury Meeting solution codeforces

For each test case, print one integer — the number of nice permutations, taken modulo 998244353998244353.

Example

input

Copy
4
2
1 2
3
5 5 5
4
1 3 3 7
6
3 4 2 1 3 3


## Jury Meeting solution codeforces

Copy
1
6
0
540