Problem Description

Ladies and gentlemen, please sit up straight.
Don't tilt your head. I'm serious.

For $n$ given strings $S_1,S_2,\cdots,S_n$, labelled from $1$ to $n$, you should find the largest $i~(1\le i\le n)$ such that there exists an integer $j~(1\le j<i)$ and $S_j$ is not a substring of $S_i$.

A substring of a string $S_i$ is another string that occurs in $S_i$. For example, ``ruiz" is a substring of ``ruizhang", and ``rzhang" is not a substring of ``ruizhang".

Input

The first line contains an integer $t~(1\le t\le 50)$ which is the number of test cases.
For each test case, the first line is the positive integer $n~(1\le n\le 500)$ and in the following $n$ lines list are the strings $S_1,S_2,\cdots,S_n$.
All strings are given in lower-case letters and strings are no longer than $2000$ letters.

Output

For each test case, output the largest label you get. If it does not exist, output $-1$.

4
5
ab
abc
zabc
abcd
zabcd
4
you
lovinyou
aboutlovinyou
allaboutlovinyou
5
de
def
abcd
abcde
abcdef
3
a
ba
ccc

Case #1: 4
Case #2: -1
Case #3: 4
Case #4: 3