Maximizing Team Knowledge Accumulation

Given a team of n people and m competitions, each person has a knowledge accumulation value (a single digit decimal number) for each competition. As a coach, you need to select k players to participate. Note that each person can participate in at most one competition, but multiple players may participate in the same competition and some players may not participate at all.

The goal is to assign exactly k players to competitions such that the sum of their knowledge accumulation values is maximized. For each selected player, you can choose the competition where they have the highest knowledge value. Mathematically, if for each player \(i\) you denote \(a_{i,j}\) as the knowledge in competition \(j\) and \(b_i=\max_{1\le j\le m}a_{i,j}\), you need to maximize the sum:

\(\sum_{i=1}^{k} b_i\)

inputFormat

The first line contains three integers: n, m, and k.

Then n lines follow, each containing m floating-point numbers (with one digit after the decimal point) representing each person's knowledge accumulation values for the m competitions.

outputFormat

Output the maximum sum of the selected k players' knowledge accumulation values, formatted as a floating-point number with one digit after the decimal point.

sample

3 2 2
5.0 6.0
7.5 6.5
4.0 8.0

15.5