시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 35 8 6 54.545%

문제

이 세상에는 남규어와 재혁어가 있다. 그러나 언제부터인가 그 중간 단계인 상학어가 발생하였다.

상학어에 속하는 단어는 다음과 같이 만들어진다. 남규어에 속하는 단어 중 하나를 골라 길이 1 이상인 접두사를 하나 고른다. 재혁어에 속하는 단어 중 하나를 골라 길이 1 이상인 접미사를 하나 고른다. 둘을 남규어-재혁어 순으로 이어붙인다. 이렇게 하면 상학어 단어가 완성된다. 참 쉽죠? 예를 들면 남규어 단어 "abc"와 재혁어 단어 "de"가 있으면 "ae", "ade", "abe", "abde", "abce", "abcde" 등의 상학어 단어를 만들 수 있지만, "bce", "ace", "abc" 등은 만들 수 없다.

물론 단어를 막 만들다 보니 때로는 의미를 부여하기 힘들 수도 있지만 그런 건 아무래도 좋다. 남규어 사전과 재혁어 사전이 주어질 때, 중복되지 않는 상학어 단어가 최대 몇 개나 만들어질 수 있는지 구하는 프로그램을 작성하시오. 예를 들면 남규어 단어 "ab", "abc"와 재혁어 단어 "cd", "d"가 있다면 "abcd"는 2번 만들어지지만 중복되므로 한 번만 세야 한다.

입력

입력은 여러 개의 테스트 케이스로 주어져 있으며, "0 0"으로 끝난다. 각 테스트 케이스는 다음과 같은 형식으로 이루어져 있다.

첫째 줄에 남규어 단어의 개수 P, 재혁어 단어의 개수 S가 주어진다. (1 ≤ P, S ≤ 1000)

그 다음 P개의 줄에 남규어 단어가 각각 하나씩, 그 다음 S개의 줄에 재혁어 단어가 각각 하나씩 주어진다. 단어는 1글자 이상 1,000글자 이하의 영어 소문자로만 이루어져 있다. 한 언어 안에 중복되는 단어는 없으며, 한 언어 안에 속하는 단어의 글자 합은 최대 105글자다.

출력

각 테스트 케이스마다 한 줄에 걸쳐 만들 수 있는 상학어 개수를 출력한다.

예제 입력 1

3 3
mais
grande
mundo
mas
grande
mundo
1 5
a
aaaaa
aaaaaa
aaaaaaa
a
aaaaaaaaa
1 1
abc
abc
0 0

예제 출력 1

182
9
8
[{"problem_id":"5683","problem_lang":"0","title":"\uc0c1\ud559\uc5b4","description":"<p>\uc774 \uc138\uc0c1\uc5d0\ub294 \ub0a8\uaddc\uc5b4\uc640 \uc7ac\ud601\uc5b4\uac00 \uc788\ub2e4. \uadf8\ub7ec\ub098 \uc5b8\uc81c\ubd80\ud130\uc778\uac00 \uadf8 \uc911\uac04 \ub2e8\uacc4\uc778 \uc0c1\ud559\uc5b4\uac00 \ubc1c\uc0dd\ud558\uc600\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\ud559\uc5b4\uc5d0 \uc18d\ud558\ub294 \ub2e8\uc5b4\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ub9cc\ub4e4\uc5b4\uc9c4\ub2e4. \ub0a8\uaddc\uc5b4\uc5d0 \uc18d\ud558\ub294 \ub2e8\uc5b4 \uc911 \ud558\ub098\ub97c \uace8\ub77c \uae38\uc774 1 \uc774\uc0c1\uc778 \uc811\ub450\uc0ac\ub97c \ud558\ub098 \uace0\ub978\ub2e4. \uc7ac\ud601\uc5b4\uc5d0 \uc18d\ud558\ub294 \ub2e8\uc5b4 \uc911 \ud558\ub098\ub97c \uace8\ub77c \uae38\uc774 1 \uc774\uc0c1\uc778 \uc811\ubbf8\uc0ac\ub97c \ud558\ub098 \uace0\ub978\ub2e4. \ub458\uc744 \ub0a8\uaddc\uc5b4-\uc7ac\ud601\uc5b4 \uc21c\uc73c\ub85c \uc774\uc5b4\ubd99\uc778\ub2e4. \uc774\ub807\uac8c \ud558\uba74 \uc0c1\ud559\uc5b4 \ub2e8\uc5b4\uac00 \uc644\uc131\ub41c\ub2e4. \ucc38 \uc27d\uc8e0? \uc608\ub97c \ub4e4\uba74 \ub0a8\uaddc\uc5b4 \ub2e8\uc5b4 &quot;abc&quot;\uc640 \uc7ac\ud601\uc5b4 \ub2e8\uc5b4 &quot;de&quot;\uac00 \uc788\uc73c\uba74 &quot;ae&quot;, &quot;ade&quot;, &quot;abe&quot;, &quot;abde&quot;, &quot;abce&quot;, &quot;abcde&quot; \ub4f1\uc758 \uc0c1\ud559\uc5b4 \ub2e8\uc5b4\ub97c \ub9cc\ub4e4 \uc218 \uc788\uc9c0\ub9cc, &quot;bce&quot;, &quot;ace&quot;, &quot;abc&quot; \ub4f1\uc740 \ub9cc\ub4e4 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\ubb3c\ub860 \ub2e8\uc5b4\ub97c \ub9c9 \ub9cc\ub4e4\ub2e4 \ubcf4\ub2c8 \ub54c\ub85c\ub294 \uc758\ubbf8\ub97c \ubd80\uc5ec\ud558\uae30 \ud798\ub4e4 \uc218\ub3c4 \uc788\uc9c0\ub9cc \uadf8\ub7f0 \uac74 \uc544\ubb34\ub798\ub3c4 \uc88b\ub2e4. \ub0a8\uaddc\uc5b4 \uc0ac\uc804\uacfc \uc7ac\ud601\uc5b4 \uc0ac\uc804\uc774 \uc8fc\uc5b4\uc9c8 \ub54c, \uc911\ubcf5\ub418\uc9c0 \uc54a\ub294 \uc0c1\ud559\uc5b4 \ub2e8\uc5b4\uac00 \ucd5c\ub300 \uba87 \uac1c\ub098 \ub9cc\ub4e4\uc5b4\uc9c8 \uc218 \uc788\ub294\uc9c0 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc608\ub97c \ub4e4\uba74 \ub0a8\uaddc\uc5b4 \ub2e8\uc5b4 &quot;ab&quot;, &quot;abc&quot;\uc640 \uc7ac\ud601\uc5b4 \ub2e8\uc5b4 &quot;cd&quot;, &quot;d&quot;\uac00 \uc788\ub2e4\uba74 &quot;abcd&quot;\ub294 2\ubc88 \ub9cc\ub4e4\uc5b4\uc9c0\uc9c0\ub9cc \uc911\ubcf5\ub418\ubbc0\ub85c \ud55c \ubc88\ub9cc \uc138\uc57c \ud55c\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc8fc\uc5b4\uc838 \uc788\uc73c\uba70, \"0 0\"\uc73c\ub85c \ub05d\ub09c\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ud615\uc2dd\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p><p>\uccab\uc9f8 \uc904\uc5d0 \ub0a8\uaddc\uc5b4 \ub2e8\uc5b4\uc758 \uac1c\uc218 P, \uc7ac\ud601\uc5b4 \ub2e8\uc5b4\uc758 \uac1c\uc218 S\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 \u2264 P, S \u2264 1000)<\/p><p>\uadf8 \ub2e4\uc74c P\uac1c\uc758 \uc904\uc5d0 \ub0a8\uaddc\uc5b4 \ub2e8\uc5b4\uac00 \uac01\uac01 \ud558\ub098\uc529, \uadf8 \ub2e4\uc74c S\uac1c\uc758 \uc904\uc5d0 \uc7ac\ud601\uc5b4 \ub2e8\uc5b4\uac00 \uac01\uac01 \ud558\ub098\uc529 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e8\uc5b4\ub294 1\uae00\uc790 \uc774\uc0c1 1,000\uae00\uc790 \uc774\ud558\uc758 \uc601\uc5b4 \uc18c\ubb38\uc790\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \ud55c \uc5b8\uc5b4 \uc548\uc5d0 \uc911\ubcf5\ub418\ub294 \ub2e8\uc5b4\ub294 \uc5c6\uc73c\uba70, \ud55c \uc5b8\uc5b4 \uc548\uc5d0 \uc18d\ud558\ub294 \ub2e8\uc5b4\uc758 \uae00\uc790 \ud569\uc740 \ucd5c\ub300 10<sup>5<\/sup>\uae00\uc790\ub2e4.<br><\/p>","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ud55c \uc904\uc5d0 \uac78\uccd0 \ub9cc\ub4e4 \uc218 \uc788\ub294 \uc0c1\ud559\uc5b4 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<br><\/p>","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5683","problem_lang":"1","title":"Diccion\u00e1rio Portu\u00f1ol","description":"<p>Portu&ntilde;ol is a special language that was naturally developed in Latin America. Since almost half of Latin America speaks Portuguese (Portugu&ecirc;s) and almost half speaks Spanish (Espa&ntilde;ol), the mixing of both languages is natural.<\/p>\r\n\r\n<p>Each word in Portu&ntilde;ol is made by taking a non-empty prefix of a Portuguese word and a nonempty suffix of a Spanish word, and concatenating them together. A prefix of a word is any word that can be obtained by erasing zero or more characters from its right end. A suffix of a word is any word that can be obtained by erasing zero or more characters from its left end. The name of the language itself comes from taking a prefix of the word &ldquo;Portugu&ecirc;s&rdquo; (Portu) and a suffix of the word &ldquo;Espa&ntilde;ol&rdquo; (&ntilde;ol), and concatenating them.<\/p>\r\n\r\n<p>Of course, not every possible way of combining two words will result in something meaningful, or even pronounceable, but that is not important. We want you to write a program to count the number of different Portu&ntilde;ol words.<\/p>\r\n\r\n<p>You will be given two non-empty sets of words to test your program. The first set will represent Portuguese words and the second set will represent Spanish words. You need to calculate the number of different Portu&ntilde;ol words that can be made using the prefix and suffix rule described above. Note that the same word may be constructed in several ways, but it still needs to be counted as one. Also note that the input sets are just to test your program, so they do not need to be made out of actual Portuguese or Spanish words.<\/p>\r\n","input":"<p>Each test case is described using several lines. The first line contains two integers P and S representing respectively the number of Portuguese words and the number of Spanish words (1 &le; P, S &le; 1000). Each of the next P lines contains a Portuguese word, and after that each of the next S lines contains a Spanish word. Each word is a non-empty string of at most 1000 characters; each character is one of the 26 standard lowercase letters (from &lsquo;a&rsquo; to &lsquo;z&rsquo;). You may assume that within each test case no two Portuguese words are the same, and that the sum of the lengths of all the Portuguese words is at most 10<sup>5<\/sup>. The same holds for the Spanish words.<\/p>\r\n\r\n<p>The last test case is followed by a line containing two zeros.<\/p>\r\n","output":"<p>For each test case output a line with an integer representing the number of different words that can be constructed by concatenating a non-empty prefix of a word in the first set (Portuguese words) and a non-empty suffix of a word in the second set (Spanish words).<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]