시간 제한메모리 제한제출정답맞힌 사람정답 비율
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문제

한중혁은 자신의 몬스터 트럭으로 도시의 절반을 날려버린 대가로 유명한 고고학자의 조수로 일하게 되었다. 그의 임무 중 하나는 고대 문서 상자의 열쇠를 만드는 일이다.

고대 문서 상자는 흥미로운 자물쇠가 달린 정교한 매커니즘으로 구성되어있다. 각각의 자물쇠는 너비 W cm, 높이 L cm 이며 상단부, 하단부, 그리고 이 둘 사이의 빈 공간으로 구성되어있다. 상단부와 하단부는 음이아닌 정수의 수열 r1, r2, r3, ..., rL로 나타내진다.

각 자물쇠에 맞는 열쇠는 가장자리 사이의 공간에 완벽하게 맞는 작은 점토 탭으로 되어있다. 아래 그림은 7cm X 8cm 형태의 자물쇠와 이에 맞는 열쇠를 나타낸다. 상단부를 나타내는 수열은 {2, 1, 3, 2, 3, 2, 3}이며 하단부를 나타내는 수열은 {3, 4, 2, 3, 2, 3, 4}이다.

한중혁은 하나의 열쇠가 두 개 이상의 자물쇠를 열 수도 있다는 것을 발견했다. 열쇠를 만드는 작업은 매우 힘들기 때문에 최소한의 열쇠로 모든 자물쇠를 열고자 한다. 한중혁의 작업을 덜어주기 위해, 최소 몇 개의 열쇠를 만들어야 하는지 알려주자.

입력

입력의 첫 번째 줄에는 자물쇠의 너비 W (1 ≤ W ≤ 108), 자물쇠의 길이 L (1 ≤ L ≤ 1000), 그리고 자물쇠의 개수 N (1 ≤ N ≤ 100)이 주어진다.

다음 2N개의 줄은 자물쇠의 정보를 나타낸다. 각 줄은 W보다 작은 L개의 수로 구성되어 있으며 상단부를 나타내는 수열과 하단부를 나타내는 수열이 주어진다. 모든 자물쇠는 상단부와 하단부 사이에 적어도 1cm의 빈 공간이 존재한다.

출력

한중혁이 만들어야 할 열쇠의 최소 개수를 출력한다.

예제 입력 1

8 7 2
2 1 3 2 3 2 3
3 4 2 3 2 3 4
3 2 4 3 4 3 4
2 3 1 2 1 2 3

예제 출력 1

1

예제 입력 2

8 4 4
3 3 3 3
3 3 3 3
2 2 2 2
4 4 4 4
1 2 3 4
4 3 2 1
1 1 1 1
5 5 5 5

예제 출력 2

2

예제 입력 3

100000000 2 2
88888888 88888888
4 4
4 4
88888888 88888888

예제 출력 3

1
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He works as an assistant for a famous archaeologist. One of his duties include crafting keys for ancient document boxes.<\/p>\r\n\r\n<p>In ancient times document boxes were locked using elaborate mechanisms with interesting locks. Each lock is L centimeters long and W centimeters wide and consists of three parts, the upper edge, the lower edge and the empty area between them. Both edges can be represented as a sequence of L nonnegative integers: r1 r2 r3 ... rL. Each number in sequence represents the width of edge at that point.<\/p>\r\n\r\n<p>The key for each lock is a small clay tab, fitting perfectly in the area between edges. This image shows a 7 cm long, 8 cm wide lock along with the corresponding key.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/8377c495-0c12-4a6b-b104-4a9637683713\/-\/preview\/\" style=\"width: 253px; height: 223px;\" \/><\/p>\r\n\r\n<p>The sequence representing the upper edge is [2, 1, 3, 2, 3, 2, 3], and the sequence representing the lower edge is [3, 4, 2, 3, 2, 3, 4]. Mirko noticed that some keys open more than one lock. Making keys is tedious work so Mirko asked you to find out what is the minimal number of different keys he needs to make and still be able to open all of the locks.<\/p>\r\n","input":"<p>First line of input contains three integers, W (1 &le; W &le; 10<sup>8<\/sup>), width of all locks, L (1 &le; L &le; 1000) length of all locks, and N (1 &le; N &le; 100), number of different locks.<\/p>\r\n\r\n<p>Next 2N lines describe all locks. Each line contains exactly L numbers smaller than W. Each pair of lines describes one lock. The first line in one pair describes the upper edge, and the second line the lower edge. There shall always be at least 1 cm of empty space between both edges on all locks.<\/p>\r\n","output":"<p>The first and only line of input should contain a single integer, the minimal number of different keys Mirko needs to craft.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

Contest > Croatian Open Competition in Informatics > COCI 2009/2010 > Contest #5 3번