Tetrahedron
TimeLimit:4500MS MemoryLimit:524288KB
64-bit integer IO format:%I64d
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Problem Description
Generate three integers $a$, $b$, and $c$ in $[1,n]$ with equal probability independently, and use them as the three right-angle side length of a right-angled tetrahedron. Find the expectation of the
reciprocal square of the distance from the right-angle apex to the slope (Euclidean distance).
For each test case, output a line containing the answer mod $998244353$.
For each test case, output a line containing the answer mod $998244353$.
Input
In the first line, you should read an integer $T$ denoting the number of test cases.
In every test case, the only line will include an integer $n$.
It is guaranteed that $T$ is no larger than $2 \times 10^6$ and $n$ is no larger than $6 \times 10^6$.
In every test case, the only line will include an integer $n$.
It is guaranteed that $T$ is no larger than $2 \times 10^6$ and $n$ is no larger than $6 \times 10^6$.
Output
For each test case, output the only line containing just one integer denoting the answer mod $998244353$.
SampleInput
3 1 2 3
SampleOutput
3 124780546 194103070