405209: GYM101845 F UN Finals

The UN finals are here!, the coaches/ex-coaches team is creating a new exciting contest to select which teams will compete in the Colombian finals. Ivan said: the rules are clear, the only limitation to enroll teams in the Colombian finals is to pick a maximum of k teams per career. A team can be labeled with career X if there is no career Y such that more team members are enrolled in career Y than in career X. Finally, each team consists of three students (as usual).

Someone in the UN campus (UN finals are pretty popular) said, hey you guys should pick the teams careers in such a way that it maximizes the number of enrolled teams. Diego said: ah that is too easy. You will prove Diego right (or wrong). Given the description of the teams, output the maximum number of teams that can be enrolled in the Colombian finals.

The first line is n (1 ≤ n ≤ 100) - the number of teams that registered to participate in the UN finals.

Next n lines contains each the information from each team, that is, there will be three strings per team (one per team member) separated by a single space. Each string consists of distinct upper case letters which represent the careers that a team member is studying (UN students love to study multiple careers).

The last line contains an integer k (1 ≤ k ≤ n) - the maximum allowed number of teams per career.

Print a single integer - the maximum number of teams that can be enrolled.

5
A ABC B
C C C
B B B
A A A
C AC CB
2

5

In the first example first and fourth team can represent career A, second and fifth team can represent career C and third can represent team B.