시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 23 17 11 78.571%

문제

보이 스카우트에서 매년 올림픽을 개최한다. 각각의 팀은 게임을 통해 점수를 얻고, 가장 높은 점수를 얻은 팀이 우승을 한다. 게임 후, 기타나 노래를 부르며 밤을 즐긴다.

올해는, 새로운 게임이 추가 될 예정이다. 게임 진영에는 N개의 나무가 있다. 각 팀은 특정 나무를 정한 뒤, 그곳에서 게임을 시작한다. 현재 나무에서 다른 나무로 이동할 때는 무조건 직선으로 가야한다. 이 게임은 시작점에 다시 돌아올 때 까지, 지나친 총 나무들의 수가 점수가 된다.

하지만, 여기에는 한 룰이 있다. 이동 할 때, 무조건 반시계 방향으로 방향회전을 해야한다는 것이다. 즉, 어떤 나무에 도달한 후에는 오직 왼쪽방향 180도 이내로만 회전하여 이동할 수 있다는 것이다.

종범이는 이 게임을 만들고, 어느 지점에 나무가 있는지까지 파악을 했다. 하지만 이 게임에서 얻을 수 있는 최대점수를 구하려고 하는데 어려움이 생겼다. 여러분의 도움이 필요하다!!

입력

첫 줄에는 나무의 수 N (3 ≤ N ≤ 100)이 자연수로 주어집니다.

각각의 N개의 줄에는 i번째 나무의 좌표로 2개의 실수 x, y (−106 ≤ x, y ≤ 106)가 공백을 사이로 두고 주어집니다. 각각의 좌표는 소수점 2째자리 이내로 주어집니다.

한 직선위에 3개 이상의 나무가 존재하지 않습니다.

출력

이 게임에서 얻을 수 있는 최대 점수를 첫 줄에 출력하세요.

예제 입력 1

5
0 0
1.5 -0.25
0 -1
-1 0.5
0.5 1

예제 출력 1

4
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