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문제

상근이와 선영이는 조금 독특한 농장을 운영하고 있다. 보통 농장에서는 동물이나 야채를 기르지만, 그들은 문자열을 기른다.

문자열은 연속되는 문자를 나타낸다. 문자열을 자라면서 왼쪽이나 오른쪽에 문자가 추가된다. 문자가 없어지는 경우는 없고, 중간에 문자가 추가되는 경우도 없다.

상근이와 선영이는 문자열의 성장 과정을 사진으로 찍었다. 하지만, 사진에 따로 적어놓은 것이 없기 때문에, 어떤 사진이 어떤 문자열의 사진인지를 까먹었다. 그들은 사진을 벽에 그들이 자란 순서대로 전시해놓으려고 한다. 자 이제 사진의 순서를 찾는 프로그램을 작성해보자.

각 사진은 문자열로 나타낼 수 있다. 사진의 순서는 반드시 다음과 같은 규칙을 지켜야 한다. si가 si+1의 바로 앞에 오려면, si+1은 si가 자란 형태이어야 한다. 즉, si가 si+1의 연속된 부분 문자열이어야 한다. 상근이와 선영이는 같은 사진을 여러 번 찍지 않는다. 따라서, 사진의 순서에 포함되는 사진은 모두 다르다.

상근이와 선영이가 찍은 사진이 입력으로 주어진다. 이 때, 가장 긴 사진의 순서를 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스의 첫째 줄에는 사진의 개수 N이 주어진다. (1 ≤ N ≤ 104) 다음 N개 줄에는 사진에 찍혀있는 문자열이 주어진다. 문자열은 알파벳 소문자로만 이루어져 있고, 길이는 1000을 넘지 않는다.

각 테스트 케이스 마다 입력으로 주어지는 문자열의 길이의 합은 106을 넘지 않는다.

입력의 마지막 줄에는 0이 하나 주어진다.

출력

각 테스트 케이스마다 가장 긴 사진의 순서의 길이를 출력한다.

예제 입력 1

6
plant
ant
cant
decant
deca
an
2
supercalifragilisticexpialidocious
rag
0

예제 출력 1

4
2
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(1 &le; N &le; 10<sup>4<\/sup>) \ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \uc0ac\uc9c4\uc5d0 \ucc0d\ud600\uc788\ub294 \ubb38\uc790\uc5f4\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ubb38\uc790\uc5f4\uc740 \uc54c\ud30c\ubcb3 \uc18c\ubb38\uc790\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \uae38\uc774\ub294 1000\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub9c8\ub2e4 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c0\ub294 \ubb38\uc790\uc5f4\uc758 \uae38\uc774\uc758 \ud569\uc740 10<sup>6<\/sup>\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ud558\ub098 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \uac00\uc7a5 \uae34 \uc0ac\uc9c4\uc758 \uc21c\uc11c\uc758 \uae38\uc774\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5699","problem_lang":"1","title":"Growing Strings","description":"<p>Gene and Gina have a particular kind of farm. Instead of growing animals and vegetables, as it is usually the case in regular farms, they grow strings. A string is a sequence of characters. Strings have the particularity that, as they grow, they add characters to the left and\/or to the right of themselves, but they never lose characters, nor insert new characters in the middle.<\/p>\r\n\r\n<p>Gene and Gina have a collection of photos of some strings at di\ufb00erent times during their growth. The problem is that the collection is not annotated, so they forgot to which string each photo belongs to. They want to put together a wall to illustrate strings growing procedures, but they need your help to \ufb01nd an appropriate sequence of photos.<\/p>\r\n\r\n<p>Each photo illustrates a string. The sequence of photos must be such that if s<sub>i<\/sub> comes immediately before s<sub>i+1<\/sub> in the sequence, then s<sub>i+1<\/sub> is a string that may have grown from s<sub>i<\/sub> (i.e., s<sub>i<\/sub> appears as a consecutive substring of s<sub>i+1<\/sub>). Also, they do not want to use repeated pictures, so all strings in the sequence must be di\ufb00erent.<\/p>\r\n\r\n<p>Given a set of strings representing all available photos, your job is to calculate the size of the largest sequence they can produce following the guidelines above.<\/p>\r\n","input":"<p>Each test case is given using several lines. The \ufb01rst line contains an integer N representing the number of strings in the set (1 &le; N &le; 10<sup>4<\/sup>). Each of the following N lines contains a di\ufb00erent non-empty string of at most 1000 lowercase letters of the English alphabet. Within each test case, the sum of the lengths of all strings is at most 10<sup>6<\/sup>.<\/p>\r\n\r\n<p>The last test case is followed by a line containing one zero.<\/p>\r\n","output":"<p>For each test case output a single line with a single integer representing the size of the largest sequence of photos that can be produced.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]