This problem is a Mooshak version of a UVA Online Judge Problem.

[PC050] Period

For each prefix of a given string \(S\) with \(N\) characters (each character is a lowercase letter), we want to know whether the prefix is a periodic string. That is, for each \(i\) \((2 \leq i \leq N)\) 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 \(N\) \((2 \leq N \leq 1\,000\,000)\) 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.

3
aaa
12
aabaabaabaab
0

Test case #1
2 2
3 3

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