**7 人解决**，13 人已尝试。

**8 份提交通过**，共有 38 份提交。

**7.4** EMB 奖励。

**单点时限: **10.0 sec

**内存限制: **256 MB

The math department has been having problems lately. Due to immense amount of unsolicited automated programs which were crawling across their pages, they decided to put Yet-Another-Public-Turing-Test-to-Tell-Computers-and-Humans-Apart on their webpages. In short, to get access to their scientific papers, one have to prove yourself eligible and worthy, i.e. solve a mathematic riddle.

However, the test turned out difficult for some math PhD students and even for some professors.Therefore, the math department wants to write a helper program which solves this task (it is not irrational, as they are going to make money on selling the program).

The task that is presented to anyone visiting the start page of the math department is as follows:

given a natural n, compute

where [x] denotes the largest integer not greater than x.

The first line contains the number of queries t (t ≤ 10^{6} ). Each query consist of one natural number n (1 ≤ n ≤ 10^{6} ).

For each n given in the input output the value of S_{n} .

Input

13 1 2 3 4 5 6 7 8 9 10 100 1000 10000

Output

0 1 1 2 2 2 2 3 3 4 28 207 1609

**7 人解决**，13 人已尝试。

**8 份提交通过**，共有 38 份提交。

**7.4** EMB 奖励。

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