lucky number 多校

lucky number

Lucky Number

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 1093    Accepted Submission(s): 167

Problem Description

   “Ladies and Gentlemen, It’s show time! ”

   “A thief is a creative artist who takes his prey in style... But a detective is nothing more than a critic, who follows our footsteps...”

   Love_Kid is crazy about Kaito Kid , he think 3(because 3 is the sum of 1 and 2), 4, 5, 6 are his lucky numbers and all others are not. 

   Now he finds out a way that he can represent a number through decimal representation in another numeral system to get a number only contain 3, 4, 5, 6. 

   For example, given a number 19, you can represent it as 34 with base 5, so we can call 5 is a lucky base for number 19. 

   Now he will give you a long number n(1<=n<=1e12), please help him to find out how many lucky bases for that number. 

   If there are infinite such base, just print out -1. 

 

Input

   There are multiply test cases.

   The first line contains an integer T(T<=200), indicates the number of cases. 

   For every test case, there is a number n indicates the number.

 

Output

   For each test case, output “Case #k: ”first, k is the case number, from 1 to T , then, output a line with one integer, the answer to the query.  

 

Sample Input

2
10
19

 

Sample Output

Case #1: 0
Case #2: 1

Hint
10 shown in hexadecimal number system is another letter different from ‘0’-‘9’, we can represent it as ‘A’, and you can extend to other cases.

 

这道题但是纠结了好久，只想想到暴力，但是复杂度太大，一定会TLE，看了题解恍然大悟，以为明白了，今天被提醒忽然发现自己理解得不是很透彻，这种以为懂了却没有好好思考记在心里的习惯要好好改改了。一定要理解到本质才行。

我们一直在思考-1 的情况发现想多了，只有再10以内的数3.4.5.6才可能在任何一种进制中仍表示为3/4/5/6，而如果大于10的就像十六进制一样，不是用数字表达了。

然后是同一数用不同的进制表达，如果进制越大，转化后的数越小