시간 제한메모리 제한제출정답맞힌 사람정답 비율
0.5 초 512 MB34962420208170.185%

문제

코딩 프로젝트 수업을 가르치는 수찬이는 프로젝트 팀을 가능하면 공정하게 구성하려고 한다. 프로젝트 팀 하나는 두 명의 학생으로 구성되는데, 각 학생들의 코딩 역량은 모두 다르다. 각 학생은 한 팀의 팀원이어야 한다. 공정성을 높이기 위해 수찬이는 팀원 코딩 역량의 합을 최대한 일정하게 유지하려고 한다. 학생들이 코딩 역량이 주어졌을 때 수찬이가 팀을 구성하는데 도움이 되는 프로그램을 작성하라.

문제를 간단하게 하기 위해, 학생 수는 2n이라 가정하자 (n은 양의 정수). 각 학생 si의 코딩 역량은 양의 정수 w(si)로 나타내면 한 i번째 팀 Gi의 코딩 역량은 w(Gi) = ∑sGiw(s)로 나타낼 수 있다. 작성할 프로그램 목적은 Sm = min{w(Gi) | 1 ≤ in}이 최대화되도록 n개의 팀 G1, G2, …, Gn 을 구성하고 이때 Sm을 출력하는 것이다.

예를 들어, 학생들의 코딩 역량이 {1, 7, 5, 8}로 주어졌다면 (8, 1), (7, 5)로 2개의 조를 짤 수 있으며 프로그램은 9를 출력해야 한다.

입력

입력은 표준입력을 사용한다. 입력의 첫 번째 행에는 팀 수를 나타내는 양의 정수 n(1 ≤ n ≤ 5,000)이 주어진다. 그 다음 행에 학생 si 의 코딩 역량 w(si)를 나타내는 2n개의 양의 정수가 공백으로 분리되어 주어진다 (1 ≤ w(si) ≤ 100,000). 학생들의 코딩 역량은 모두 다르다. 즉, ij이면 w(si) ≠ w(sj)이다.

출력

출력은 표준출력을 사용한다. 표준출력 한 행에 Sm을 출력한다.

예제 입력 1

2
1 7 5 8

예제 출력 1

9

예제 입력 2

3
1 7 3 5 9 2

예제 출력 2

8
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