题目
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).
Input
The first line contains the number of queries t (t ≤ 10^6). Each query consist of one natural number n (1 ≤n ≤10^6).
Output
For each n given in the input output the value of Sn.
Sample Input
13
1
2
3
4
5
6
7
8
9
10
100
1000
10000
Sample Output
0
1
1
2
2
2
2
3
3
4
28
207
1609
然而，对于一些数学博士生甚至一些教授来说，测试结果很难。 因此，数学系想要编写一个帮助程序来解决这个任务（这不是不合理的，因为他们会在出售程序时赚钱）。
代码如下:
#include
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