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

输入描述:

The input consists of several test cases. Each test case consists of two lines. The first one contains N – 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.

输出描述:

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.

3
aaa
12
aabaabaabaab
0

Test case #1
2 2
3 3

Test case #2
2 2
6 2
9 3
12 4