Description

For each prefix of a given string S with N characters (each character has an ASCII code between 97 and 126, inclusive), we want to know whether the prefix is a periodic string. That is, for each i (2 <= i <= N) we want to know the largest K > 1 (if there is one) such that the prefix of S with length i can be written as A

^K , that is A concatenated K times, for some string A. Of course, we also want to know the period K.

 

Input

The input file consists of several test cases. Each test case consists of two lines. The first one contains N (2 <= N <= 1 000 000) � the size of the string S. The second line contains the string S. The input file ends with a line, having the number zero on it.

 

Output

For each test case, output “Test case #” and the consecutive test case number on a single line; then, for each prefix with length i that has a period K > 1, output the prefix size i and the period K separated by a single space; the prefix sizes must be in increasing order. Print a blank line after each test case.

 

Sample Input

3

aaa

12

aabaabaabaab

0

 

Sample Output

Test case #1

2 2

3 3

Test case #2

2 2

6 2

9 3

12 4

KMP的前缀函数处理出来的前缀数组表示当当前字符失配后，要向前调到哪一个位置可以继续匹配。也就是代表着跳到的那个位置之前的所有字符与当前失配字母前的相同数量个字母是相匹配的。

也是KMP中循环节的模板题

1 #include 
         
           2 #include 
          
            3 #include 
           
             4 const int N=1000100; 5 char a[N],b[N]; 6 int len,n[N]; 7 void next() 8 { 9     int i=0;10     int j=-1;11     n[0]=-1;12     while(i