Cube Summation

TimeLimit:5000MS MemoryLimit:153428KB

64-bit integer IO format:%I64d

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Problem Description

Given an integer N, consider all multi-sets of positive integers such that their sum is N.
For example, if N =3, there are three possible multi-sets {1, 1, 1}, {1, 2}, {3}.
For each multi-set calculate the cube of its size and output the sum of all these values modulo 998244353.

Input

The first line of input contains an integer T (1<= T <=10000), the number of test cases.
Each test case contains a single integer N (1<= N<=100000).

Output

For each test case, output one line with a single integer, denoting the answer to the problem.

SampleInput

SampleOutput

1
9
36
513842114
 Hint For the 1st case, the only possible multi-set is {1}. So the answer is 1^3=1. For the 2nd case, there are 2 possible multi-sets. {1, 1}, {2}. So the answer is 2^3+1^3=9. For the 3rd case, there are 3 possible multi-sets. {1, 1, 1}, {1, 2}, {3}. So the answer is 3^3+2^3+1^3=36.

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题目统计信息详细


总AC数	0
通过人数	0
尝试人数	0
总提交量	0
AC率	0.00%

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出处

【每日一题】2019年1月

Cube Summation

T^T Online Judge