问题 D: 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≤�≤1091≤n≤109).

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 $q\not\equiv 0\mathrm{mod}998244353$, and there is a unique integer $r$ satisfies $0\le r<998244353$ and $qr\equiv p\mathrm{mod}998244353$. Find this $r$.

2
1
2

0
1