시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 3 2 2 66.667%

문제

프로그래밍 대회는 대회마다 나오는 문제의 유형이 다르다. 예를 들어, TopCoder는 배열의 최대 크기가 50이다. 또, IOI는 아이들이 참가하는 대회이기 때문에 Suffix Tree문제는 나오지 않는다.

우현이는 서로 다른 N개 프로그래밍 대회의 문제 출제자이다. 각 대회는 필요한 문제의 수가 서로 다르다. 예를 들어, ACM-ICPC 스타일의 대회는 보통 10 문제가 필요하고, Topcoder SRM은 5문제가 필요하다.

다행히도 우현이는 M개 문제를 미리 준비해두었다. 또, 각 문제 별로 어떤 대회에서 사용할 수 있는지도 정해놓았다.

모든 대회를 전부 동시에 진행할 때, 몇 개의 대회를 진행할 수 있을까? 대회를 진행하려면 필요한 문제수 만큼 모두 준비해야 한다. 또, 한 문제를 서로 다른 대회에 출제할 수 없다.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 

테스트 케이스의 첫째 줄에는 대회의 수 N과 준비한 문제의 수 M이 주어진다. (1 ≤ N ≤ 15, 0 ≤ M ≤ 50) 다음 N개의 줄에는 각 대회의 이름과 대회를 열기 위해 필요한 문제 수가 주어진다. 대회의 이름은 알파벳 대소문자와 숫자로 이루어져 있고, 100자를 넘지 않는다. 또, 알파벳 대소문자를 구분한다. 필요한 문제 수는 100개를 넘지 않는다.

다음 M개의 줄에는 각 문제를 낼 수 있는 대회의 이름이 공백으로 구분되어 주어진다. 만약, 어떤 문제를 낼 수 있는 대회가 없을 때는 비어있다.

입력의 마지막 줄에는 0 두 개가 주어진다.

출력

각 테스트 케이스에 대해서, 동시에 개최할 수 있는 대회의 수를 케이스 번호와 함께 출력한다. 예제 출력 형식을 참고한다.

예제 입력 1

4 5
IOI 3
IPSC 2
TopCoder 2
SEERC 10
IOI
IPSC TopCoder
IOI IPSC
IOI IPSC
TopCoder SEERC
1 1
SampleContest 1
SampleContest
0 0

예제 출력 1

Case #1: 2
Case #2: 1
[{"problem_id":"3727","problem_lang":"0","title":"\ud504\ub85c\uadf8\ub798\ubc0d \ub300\ud68c","description":"<p>\ud504\ub85c\uadf8\ub798\ubc0d \ub300\ud68c\ub294 \ub300\ud68c\ub9c8\ub2e4 \ub098\uc624\ub294 \ubb38\uc81c\uc758 \uc720\ud615\uc774 \ub2e4\ub974\ub2e4. \uc608\ub97c \ub4e4\uc5b4, TopCoder\ub294 \ubc30\uc5f4\uc758 \ucd5c\ub300 \ud06c\uae30\uac00 50\uc774\ub2e4. \ub610, IOI\ub294 \uc544\uc774\ub4e4\uc774 \ucc38\uac00\ud558\ub294 \ub300\ud68c\uc774\uae30 \ub54c\ubb38\uc5d0 Suffix Tree\ubb38\uc81c\ub294 \ub098\uc624\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc6b0\ud604\uc774\ub294 \uc11c\ub85c \ub2e4\ub978 N\uac1c \ud504\ub85c\uadf8\ub798\ubc0d \ub300\ud68c\uc758 \ubb38\uc81c \ucd9c\uc81c\uc790\uc774\ub2e4. \uac01 \ub300\ud68c\ub294 \ud544\uc694\ud55c \ubb38\uc81c\uc758 \uc218\uac00 \uc11c\ub85c \ub2e4\ub974\ub2e4. \uc608\ub97c \ub4e4\uc5b4, ACM-ICPC \uc2a4\ud0c0\uc77c\uc758 \ub300\ud68c\ub294 \ubcf4\ud1b5 10 \ubb38\uc81c\uac00 \ud544\uc694\ud558\uace0, Topcoder SRM\uc740 5\ubb38\uc81c\uac00 \ud544\uc694\ud558\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\ud589\ud788\ub3c4 \uc6b0\ud604\uc774\ub294 M\uac1c \ubb38\uc81c\ub97c \ubbf8\ub9ac \uc900\ube44\ud574\ub450\uc5c8\ub2e4. \ub610, \uac01 \ubb38\uc81c \ubcc4\ub85c \uc5b4\ub5a4 \ub300\ud68c\uc5d0\uc11c \uc0ac\uc6a9\ud560 \uc218 \uc788\ub294\uc9c0\ub3c4 \uc815\ud574\ub193\uc558\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ub300\ud68c\ub97c \uc804\ubd80 \ub3d9\uc2dc\uc5d0 \uc9c4\ud589\ud560 \ub54c, \uba87 \uac1c\uc758 \ub300\ud68c\ub97c \uc9c4\ud589\ud560 \uc218 \uc788\uc744\uae4c? \ub300\ud68c\ub97c \uc9c4\ud589\ud558\ub824\uba74 \ud544\uc694\ud55c \ubb38\uc81c\uc218 \ub9cc\ud07c \ubaa8\ub450 \uc900\ube44\ud574\uc57c \ud55c\ub2e4. \ub610, \ud55c \ubb38\uc81c\ub97c \uc11c\ub85c \ub2e4\ub978 \ub300\ud68c\uc5d0 \ucd9c\uc81c\ud560 \uc218 \uc5c6\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \ub300\ud68c\uc758 \uc218 N\uacfc \uc900\ube44\ud55c \ubb38\uc81c\uc758 \uc218 M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; N &le; 15, 0 &le; M &le; 50) \ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \ub300\ud68c\uc758 \uc774\ub984\uacfc \ub300\ud68c\ub97c \uc5f4\uae30 \uc704\ud574 \ud544\uc694\ud55c \ubb38\uc81c \uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub300\ud68c\uc758 \uc774\ub984\uc740 \uc54c\ud30c\ubcb3 \ub300\uc18c\ubb38\uc790\uc640 \uc22b\uc790\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, 100\uc790\ub97c \ub118\uc9c0 \uc54a\ub294\ub2e4. \ub610, \uc54c\ud30c\ubcb3 \ub300\uc18c\ubb38\uc790\ub97c \uad6c\ubd84\ud55c\ub2e4. \ud544\uc694\ud55c \ubb38\uc81c \uc218\ub294 100\uac1c\ub97c \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c M\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \ubb38\uc81c\ub97c \ub0bc \uc218 \uc788\ub294 \ub300\ud68c\uc758 \uc774\ub984\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. \ub9cc\uc57d, \uc5b4\ub5a4 \ubb38\uc81c\ub97c \ub0bc \uc218 \uc788\ub294 \ub300\ud68c\uac00 \uc5c6\uc744 \ub54c\ub294 \ube44\uc5b4\uc788\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0 \ub450 \uac1c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \ub3d9\uc2dc\uc5d0 \uac1c\ucd5c\ud560 \uc218 \uc788\ub294 \ub300\ud68c\uc758 \uc218\ub97c \ucf00\uc774\uc2a4 \ubc88\ud638\uc640 \ud568\uaed8 \ucd9c\ub825\ud55c\ub2e4. \uc608\uc81c \ucd9c\ub825 \ud615\uc2dd\uc744 \ucc38\uace0\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3727","problem_lang":"1","title":"Problemsetting","description":"<p>It&#39;s well-known that different programming contests require different kind of problems. For example, maximal array size for TopCoder problem is only 50, and you definitely can not give a Suffix Tree problem to IOI because children will not have a chance to solve it (except of some touristic-inclined ones). Thus not every problem is acceptable for every contest.<\/p>\r\n\r\n<p>You are preparing problemsets for N different contests. These contests require different number of problems, depending of type. For example, ACM ICPC style problemset usually has 10 problems, TopCoder SRM &ndash; 5 and so on.<\/p>\r\n\r\n<p>Luckily you have already prepared M different problems. For each problem you have determined a set of contests you can give that problem to. Also you know the required number of problems for each contest.&nbsp;<\/p>\r\n\r\n<p>Find out the maximal number of different contests for which you can simultaneously compose complete problemsets from the given set of problems. All problems in the problemsets must be unique, i.e. no problem can be used twice in different problemsets.<\/p>\r\n","input":"<p>The input file contains several test cases.&nbsp;<\/p>\r\n\r\n<p>The first line of each test case contains 2 integers N and M (1 &le; N &le; 15, 0 &le; M &le; 50) &ndash; the number of different contests and the number of prepared problems. Each of the following N lines contains the name of contest, followed by the required number of problems for that contest. The name of a contest consists of lower- and uppercase Latin letters and\/or digits, is not empty and does not exceed 100 characters. Contest names are case-sensitive. It&#39;s guaranteed that all contest names will be pairwise different. The required number of problems does not exceed 100.&nbsp;<\/p>\r\n\r\n<p>Each of the following M lines contains a (possibly empty) list of acceptable contest names for each problem, separated by a single space. It&#39;s guaranteed that all contest names will be correct (i.e., noted in the previous section of the current test case) and unique.&nbsp;<\/p>\r\n\r\n<p>The line containing two zeroes indicates the end of the input file.<\/p>\r\n","output":"<p>For each test case print an answer for that case on a new line, as shown in the sample output.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]