write a go solution for Description:
There is a hidden array a of size n consisting of only 1 and -1. Let p be the prefix sums of array a. More formally, p is an array of length n defined as p_i=a_1+a_2+ldots+a_i. Afterwards, array p is sorted in non-decreasing order. For example, if a=[1,-1,-1,1,1], then p=[1,0,-1,0,1] before sorting and p=[-1,0,0,1,1] after sorting.

You are given the prefix sum array p after sorting, but you do not know what array a is. Your task is to count the number of initial arrays a such that the above process results in the given sorted prefix sum array p. As this number can be large, you are only required to find it modulo 998,244,353.

Input Format:
Each test contains multiple test cases. The first line contains a single integer t (1<=t<=1000) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer n (1<=n<=5000) — the size of the hidden array a.

The second line of each test case contains n integers p_1,p_2,ldots,p_n (|p_i|<=n) — the n prefix sums of a sorted in non-decreasing order.

It is guaranteed that p_1<=p_2<=ldots<=p_n.

It is guaranteed that the sum of n over all test cases does not exceed 5000.

Output Format:
For each test case, output the answer modulo 998,244,353.

Note:
In the first two test cases, the only possible arrays a for n=1 are a=[1] and a=[-1]. Their respective sorted prefix sum arrays p are p=[1] and p=[-1]. Hence, there is no array a that can result in the sorted prefix sum array p=[0] and there is exactly 1 array a that can result in the sorted prefix sum array p=[1].

In the third test case, it can be proven that there is no array a that could result in the sorted prefix sum array p=[-1,1,2].

In the fourth test case, the 3 possible arrays a that could result in the sorted prefix sum array p=[-1,0,0,1,1] are:

- a=[1,-1,1,-1,-1]. The prefix sum array before sorting is p=[1,0,1,0,-1], which after sorting gives p=[-1,0,0,1,1].
- a=[1,-1,-1,1,1]. The prefix sum array before sorting is p=[1,0,-1,0,1], which after sorting gives p=[-1,0,0,1,1].
- a=[-1,1,1,-1,1]. The prefix sum array before sorting is p=[-1,0,1,0,1], which after sorting gives p=[-1,0,0,1,1].

For the fifth test case, the only possible array a that could result in the sorted prefix sum array p=[-4,-3,-3,-2,-1] is a=[-1,-1,-1,-1,1].. Output only the code with no comments, explanation, or additional text.