문제
은하는 긴 막대에 $N$개의 과일이 꽂혀있는 과일 탕후루를 만들었습니다. 과일의 각 종류에는 1ドル$부터 9ドル$까지의 번호가 붙어있고, 앞쪽부터 차례로 $S_1, S_2, \cdots, S_N$번 과일이 꽂혀있습니다. 과일 탕후루를 다 만든 은하가 주문을 다시 확인해보니 과일을 두 종류 이하로 사용해달라는 요청이 있었습니다.
탕후루를 다시 만들 시간이 없었던 은하는, 막대의 앞쪽과 뒤쪽에서 몇 개의 과일을 빼서 두 종류 이하의 과일만 남기기로 했습니다. 앞에서 $a$개, 뒤에서 $b$개의 과일을 빼면 $S_{a+1}, S_{a+2}, \cdots, S_{N-b-1}, S_{N-b}$번 과일, 총 $N-(a+b)$개가 꽂혀있는 탕후루가 됩니다. $(0 \le a, b;$ $a+b < N)$
이렇게 만들 수 있는 과일을 두 종류 이하로 사용한 탕후루 중에서, 과일의 개수가 가장 많은 탕후루의 과일 개수를 구하세요.
출력
문제의 방법대로 만들 수 있는 과일을 두 종류 이하로 사용한 탕후루 중에서, 과일의 개수가 가장 많은 탕후루의 과일 개수를 첫째 줄에 출력하세요.
과일을 앞에서 1ドル$개, 뒤에서 0ドル$개의 과일을 빼면 남은 과일은 1,ドル 1, 2, 1$번 과일이 꽂혀있는 탕후루가 됩니다. 과일의 개수는 4ドル$개입니다.
탕후루가 이미 두 종류 이하의 과일로만 이루어져 있습니다.
과일을 앞에서 3ドル$개, 뒤에서 4ドル$개의 과일을 빼면 남은 과일은 4,ドル 5$번 과일이 꽂혀있는 탕후루가 됩니다. 과일의 개수는 2ドル$개입니다.
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