Passwords

The secret server of ICPC (Inter-Continental Programming Company) uses two passwords $v$ and $w$. The two strings satisfy $v^{|w|} = w^{|v|}$, which means that $v$ concatenated $|w|$ times and $w$ concatenated $|v|$ times give the same string, where $|v|$ is the length of the string $v$. For example, with $v = \mathtt{ab}$ and $w = \mathtt{abab}$ you get $v^{4} = w^{2} = \mathtt{abababab}$. The trivial case $v = w$ is not secure, so it is never used.

The two strings are hard to memorize, so the administrator hid them in a set of $n$ strings. The set contains two distinct strings $x$ and $y$ such that $v$ is a prefix of $x$ ($x = vv'$) and $w$ is a suffix of $y$ ($y = w'w$).

Given the set of strings, write a program that finds the password pair.

Your program reads from standard input. The first line contains the number of test cases $T$.

Each test case begins with a line containing $n$, the number of strings in the set. ($2 \le n \le 200$)

Each of the next $n$ lines contains one string. Every string consists of lowercase English letters and its length is at most $20{,}000$.

Your program writes to standard output. Print exactly one line for each test case.

Each line contains two integers $|v|$ and $|w|$, where two distinct strings $x$ and $y$ of the set satisfy that $v$ is a prefix of $x$, $w$ is a suffix of $y$, $v^{|w|} = w^{|v|}$ and $|v| < |w|$. If two or more such pairs exist, print the one whose $|v| + |w|$ is the greatest. Such a password pair is unique whenever it exists. If there is no such pair, print 0 0.