OpenKattis
National University of Singapore

Tournament

Every September, the Kingdom of Loowater holds a jousting tournament. In each of a series of events, a pair of knights attempt to knock each other from their respective horses. The winning knight is paired with another, while the loser is eliminated. This process continues until all but one knight is eliminated; this knight is declared champion.

The tournament schedule is organized so that no knight needs to compete in more than $e$ events to be champion, for the minimum possible $e$ given $k$, the number of knights. In order to construct the schedule, it may be necessary to identify several knights who compete in fewer than $e$ events; these knights are said to be awarded a bye and are excluded from the first round of competition.

The first round of competition involves pairing as many knights as possible among those who are not awarded a bye. The competition is more interesting if the knights in each pair are as evenly matched in ability as possible. You are to determine which knights should be awarded a bye so as to make the first round as interesting as possible.

Input

Standard input consists of several test cases (at most $10$) followed by a line containing $0$. Each test case begins with an integer $2 \le k \le 2500$, the number of knights. $k$ lines follow, each giving the name and ability of a knight. The name is a nonempty string of lower case letters not longer than $20$; the ability is an integer between $0$ and $10\, 000$. No two names in a test case are equal.

The mismatch between knights with abilities $a$ and $b$ respectively is defined to be $(a-b)^2$.

Output

For each test case, output the number of knights to be given a bye, followed by their names. The knights to be given a bye should be chosen such that the sum of all mismatch values for pairs of knights competing in the first round is minimized (assuming these are paired up in an optimal way). If there are several solutions, any will do.

Sample Input 1 Sample Output 1
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