Golden Tickets

There are $N$ teams participating in INC 2023. The team ranked $i$th is team $S_i$, representing institution $T_i$. The top $M$ teams in INC 2023 are eligible to participate in The ICPC Asia Jakarta 2023.

Apart from the top $M$ teams, Golden Tickets are given to at most the top $K$ teams whose institutions are not in the top $M$ of INC 2023. Each institution receives at most one Golden Ticket, and only the highest-ranked team from each institution qualifies. Teams that receive a Golden Ticket can participate in The ICPC Asia Jakarta 2023.

Determine the number of teams that receive Golden Tickets. Then output the names of those teams, sorted by rank.

The first line contains three integers $N$, $M$, $K$ ($1 \le M, K \le N \le 100$).

Each of the next $N$ lines contains two strings $S_i$ and $T_i$ separated by a space ($1 \le |S_i|, |T_i| \le 10$). All strings consist of uppercase letters. No two teams have the same name, so $S_i \ne S_j$ for $1 \le i < j \le N$.

On the first line, print the number $X$ of teams that receive Golden Tickets. Then print $X$ lines, each containing the name of one such team, sorted by rank. If $X = 0$, print no names.

Disclaimer

All team names and institution names in the samples are fictional. Any similarities with actual participants in INC 2023 are purely coincidental.