Personality Test

There are $n$ students taking a personality test consisting of $m$ questions. The students are numbered from $1$ to $n$ and the questions are numbered from $1$ to $m$. For each question, each student can either answer it with a single uppercase Latin character (A–Z) or not answer it. Let $S_i$ be a string of $m$ characters representing the answers of student $i$, where the $j$-th character of $S_i$ is an uppercase Latin character if they answered question $j$, or a period (.) if they did not.

Two students are considered similar if there is a set of at least $k$ questions where both students answered all questions in the set, and for each question in the set, they answered it with the same answer.

For example, let $n = 3$, $m = 3$, $k = 2$, $S_1 =$ BBC, $S_2 =$ ..C, and $S_3 =$ .BC. In this example, students $1$ and $3$ are similar since they answered questions $2$ and $3$ with the same answer, while students $2$ and $3$ are not similar since they answered only question $3$ with the same answer.

You want to find a pair of integers $(a, b)$ such that $a < b$ and students $a$ and $b$ are similar, or determine if there is no such pair. If there is more than one pair, find the one with the smallest $b$. If there is still more than one pair, find the one with the largest $a$.

The first line of input contains three integers $n$, $m$, and $k$ ($2 ≤ n ≤ 5000$; $1 ≤ m ≤ 3000$; $1 ≤ k ≤ 5$). Each of the next $n$ lines contains a string of $m$ characters. The $i$-th line contains the string $S_i$.

Output one line containing the integers $a$ and $b$ representing the pair of similar students as mentioned in the problem statement, or just the integer -1 if there is no such pair.