P11770 Eaves cloaked in snow

*The rain taps against the windowsill, cascading down, step by step, in a poetic dance.* But it's snow! Leaning against the window, Tianyi and Ling admire the suddenly arrived flurries of snow.

Still in the familiar place: there are a total of $n$ window ledges, numbered from top to bottom, with the topmost being numbered $1$ and the bottommost being numbered $n$. Tianyi notices that the snow accumulations on each ledge can be viewed as a multiset of snowballs, where initially, the first ledge holds a single snowball with a volume of $1$, while the other ledges are devoid of any snow. Suddenly, a gust of wind laden with snow blows through, instigating $n$ transformations in the snow accumulations - In the $i$-th transformation, **every** snowball on the $i$-th ledge is lifted up. Due to peculiar physical phenomena, all ledges whose numbers are multiples of $i$ (**excluding** $i$ itself) receive new snow accumulations. Specifically, let the volume of a lifted snowball be $V$. Among these receiving ledges, the one with the largest number receives a snowball of volume $V+1$, the second largest receives a snowball of volume $V+2$, and so on. In the end, the lifted snowball mysteriously returns to the $i$-th ledge, leaving the snow accumulation on the $i$-th ledge unchanged after this transformation. Ling knows that Tianyi is intrigued by the question: After the $n$ transformations, what is the total volume of **the largest** snowball on each ledge? As they sit peacefully admiring the snow, you are tasked with answering this question for them.

The first line of the input contains an integer $T$ — the number of test cases. The only line of each test case contains an intergers $n$ — the number of window ledges.

For each test case, output a single integer — the total volume of the largest snowball on each ledge.

### Sample Explanation The final state when $n=5$ is as follows: On the first ledge is a snowball with a volume of $1$; On the second ledge is a snowball with a volume of $5$; On the third ledge is a snowball with a volume of $4$; On the fourth ledge are two snowballs with volumes of $3,6$; On the fifth ledge is a snowball with a volume of $2$; The total volume of the largest snowball on each ledge is $1+5+4+6+2=18$. ### Constrains **Subtasks applied.** You can only gain the score of the subtask if you accepted all the tests in the subtask. | Subtask ID | $T\leq$ | $n\leq$ | Score | | :---: | :---: | :---: | :---: | | 1 | $100$ | $ 3\times10^4$ | $15$ | | 2 | $ 100$ | $ 2\times10^6$ | $35$ | | 3 | $ 3\times10^4$ | $ 3\times10^4$ | $15$ | | 4 | $ 2\times10^5$ | $ 2\times10^5$ | $15$ | | 5 | $ 5\times10^5$ | $ 2\times 10^6$ | $20$ | For all tests, it is guaranteed that $1\le T\le5\times10^5$，$1\le n\le2\times10^6$.