P8574 "DTOI-2" Shadow of the Stars

>It is said to be the White Polar Shadow; when you see it, only then does the pole stand.

The White Polar Shadow turns into the Pole-Standing Man and comes to the human world, bringing the star function $f(x)$, whose value is the integer closest to $\sqrt[4]x$ $\\$ (that is, $f(x)=\left\lfloor\sqrt[4]x+\dfrac12\right\rfloor$; $\lfloor u\rfloor$ is the value of $u$ rounded down). Now there are $t$ numbers $n$. For each $n$, the Pole-Standing Man wants to know the value of $\sum\limits_{i=1}^n\dfrac1{f(i)}$. Please tell it. --- ~~Because the Pole-Standing Man is in a hurry,~~ the $t$ queries in this problem are forced online: each later query must be generated using the answer to the previous query. You can generate them with the following `C++` code (same idea for other languages; you need to include ``): ```cpp typedef long long ll; char buf_ans[114]; ll next_n(double last_ans=0,ll get_n=0){ //last_ans

The first line contains an integer $t$, indicating the number of datasets (number of queries). For each dataset, there is only one line containing an integer, representing the encrypted $n$ (the first $n$ is not encrypted).

Output one line per query, a number with exactly six digits after the decimal point, representing the answer.

### Sample Explanation After decryption, the queries in sample #1 are: $$ \def\r{\cr\hline} \def\arraystretch{1.5}\begin{array}{|c|c|c|c|c|c|c|c|}\hline \textbf{t}&1&2&3&4&5&6&7\r \textbf{n}&1&4&8&89&2022&1145141919810&1\r \end{array} $$ ### Constraints **This problem uses bundled tests.** $$ \def\arraystretch{1.5}\begin{array}{|c|c|c|c|}\hline \textbf{Subtask} & t= & n\le&\bm{\textbf{Score}} \cr\hline 1 & 10&10^6 & 2 \cr\hline 2&1000&10^6&13\cr\hline 3&100&10^9&15\cr\hline 4 &1000&10^{18}&40\cr\hline 5 &%\text{No Special Constraints} 5\times10^5&10^{18}& 30 \cr\hline \end{array} $$ For $100\%$ of the testdata, $10 \le t \le 5\times10^5$, $1 \le n \le 10^{18}$. ### Scoring Rules This problem uses a $\textbf{Special Judge}$. Let the answer you output be $\text{pans}$ and the standard answer be $\text{jans}$. If $\vert \text{pans}-\text{jans}\vert