ACM 数论 HDU 2973 YAPTCHA 威尔逊定理

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.

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

Source

Central European Programming Contest 2008

这道题非常像一道高数题,学会转化!

令t=3*k+7;

把原式化简...

威尔逊定理:如果9为质数,那么p可以整除(p-1)!+1; 也就是[(p-1)!+1]/p=0

正好和化简后的原式部分相同;

那么这道题就变成了判断t是否为质数,是的话就+1