Personality Test

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

Two students are similar if there is a set of at least $k$ questions such that both students answered every question in the set, and for each question in the set they gave the same answer. For example, with $n = 3$, $m = 3$, $k = 2$, $S_1$ = BBC, $S_2$ = ..C, and $S_3$ = .BC, students 1 and 3 are similar because they gave the same answers to questions 2 and 3. Students 2 and 3 are not similar because they share only one matching question (question 3).

You want to find a pair of integers $(a, b)$ with $a < b$ such that students $a$ and $b$ are similar, or determine that no such pair exists. If several pairs exist, pick the one with the smallest $b$. If there is still a tie, pick the one with the largest $a$.

The first line contains three integers $n$, $m$, and $k$ ($2 \le n \le 5000$, $1 \le m \le 3000$, $1 \le k \le 5$). 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 $b$ for a similar pair, as described in the problem. If no such pair exists, output the integer -1.