Find the C-th Best Team

In this problem, two neighboring cities send a team of exactly $K$ contestants to participate in $K$ competitions every year. Each contestant takes part in all $K$ competitions. For each competition, the team’s score is determined by the highest score obtained by any team member in that competition. The total team score is the sum of the scores from all $K$ competitions.

A team is formed by selecting exactly $K$ candidates out of $n$ available candidates. Two teams are considered different if and only if they differ in at least one member. The teams are then ranked in descending order according to their total scores (the team with the highest score is ranked 1, the second highest is ranked 2, and so on). Your task is to find the total score of the $C$-th best team.

The input begins with three integers $n$, $K$, and $C$, where $n$ is the number of candidates, $K$ is both the number of competitions and the team size, and $C$ represents the rank of the team to retrieve (with $C = 1$ being the best team). Each of the following $n$ lines contains $K$ integers, with the $j$-th integer in the $i$-th line representing the score of candidate $i$ in competition $j$.

inputFormat

The first line contains three integers: $n$ (the number of candidates), $K$ (the number of competitions and the number of contestants in each team), and $C$ (the rank of the team to find, where $C = 1$ is the best team).
Each of the next $n$ lines contains $K$ integers, where the $j$-th integer is the score for that candidate in competition $j$.

outputFormat

Output a single integer representing the total score of the $C$-th best team.

sample

3 3 1
4 5 3
7 3 6
3 4 5

18