Parentheses sequence of length 2n is the sequence containing exactlyn opening parentheses «(» and exactlyn closing parentheses «)»
A parentheses sequence is called balanced if one can turn it into a valid math expression by adding characters «+» and «1». For example, sequences «(())()», «()» and «(()(()))» are balanced, while «)(», «(()» and «(()))(» are not.
A parentheses sequence, s of length 2n is called interesting if one can turn it balanced by doing the following operation at most once.
Select two indices i,j(1≤i,j≤2n) and swap s[i] and s[j].
You have to calculate the number of different interesting parentheses sequence of length 2n, and print it modulo 998244353.
First line will contain T(1≤T≤103), the number of test cases. Each of the next T lines will contain one integer n(1≤n≤103), half the length of the interesting parentheses sequence.
For each testcase, print one line containing an integer ans(0≤ans<998244353), which is the number of different interesting parentheses sequence modulo 998244353.
In the first test case, there are 2 interesting parentheses sequence, these are as follows.
In the second test case, there 6 interesting parentheses sequence, these are as follows.