Do You Like Interactive Problems?

There is an integer $x$ satisfying $1\le x\le n$. You know $n$ but you don't know $x$.

You can do the following guessing: pick an random integer $y$ uniformly satisfying $1\le y\le n$ (your $y$ may equal to previous queries), and you will be told if $x< y$, $x> y$ or $x=y$. You will stop asking if there is only one possible $x$ satisfying all the conditions.

Given $n$, if $x$ is picked randomly uniformly, what's your expected number of queries?

The first line contains an integer $T$ ($1\le T\le 100$) denoting the number of test cases.

For each test case, the only line contains an integer $n$ ($1\le n\le 10^9$).

For each test case, output one integer denoting the expected number of queries modulo $998244353$.

Formally, it can be proven that the sought expected value can be represented as an irreducible fraction $p/q$ which satisfies $q\not\equiv 0\bmod{998244353}$, and there is a unique integer $r$ satisfies $0\le r<998244353$ and $qr\equiv p\bmod{998244353}$. Find this $r$.

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2023“钉耙编程”中国大学生算法设计超级联赛（10）