시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB190342829.167%

문제

생물학자를 꿈꾸는 강산이는 새해 선물로 현미경을 받았다. 

어느 날, 물 속에 있는 박테리아의 움직임을 관찰하고 있었다. 관찰을 한 시간 정도 하다보니, 일정한 규칙대로 움직인다는 것을 알 수 있었다.

물방울은 크기가 무한대인 정사각형 격자로 모델링 할 수 있다. 박테리아는 한 정사각형에 있다. 박테리아가 움직이는 방향은 다음과 같이 숫자로 표현할 수 있다.

1 2 3
8 B 4
7 6 5

모든 박테리아는 동시에 움직이고, 1초 단위로 움직이고, 한 방향으로만 움직인다. 박테리아 여러 마리가 같은 칸에 있을 수도 있다.

박테리아의 위치와 움직이는 방향이 주어졌을 때, 박테리아 여러 마리가 같은 칸에 제일 많이 있을 때가 언제인지, 그리고 그 때 몇 마리가 같은 칸에 있었는지 구하는 프로그램을 작성하시오. 만약 이러한 최댓값이 여러개라면, 가장 빠른 시간을 출력한다.

입력

첫째 줄에 박테리아의 수 N(1 ≤ N ≤ 5,000)이 주어진다.다음 N개의 줄에는 세 개의 정수 X, Y, D (-1,000,000 ≤ X,Y ≤ 1,000,000), (1 ≤ D ≤ 8) 가 주어진다. 

X와 Y는 박테리아의 시작 좌표이며, D는 방향이다. X값은 왼쪽에서 오른쪽으로 갈 수록 증가하며, Y값은 위로 갈수록 증가한다.

박테리아의 시작 위치가 겹치는 경우는 없으며, 적어도 한 번은 박테리아가 만난다.

출력

첫째 줄에 박테리아가 같은 칸에 가장 많이 있었을 때, 몇 마리나 있었는지 출력한다. 둘째 줄에는 그 때의 시간을 출력한다.

예제 입력 1

4
2 2 2
2 3 6
5 1 2
5 9 6

예제 출력 1

2
4

예제 입력 2

5 
1 1 1 
-6 0 3 
-2 0 2 
1 7 7 
-6 4 4

예제 출력 2

3 
4
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X\uac12\uc740 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \uac08 \uc218\ub85d \uc99d\uac00\ud558\uba70, Y\uac12\uc740 \uc704\ub85c \uac08\uc218\ub85d \uc99d\uac00\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubc15\ud14c\ub9ac\uc544\uc758 \uc2dc\uc791 \uc704\uce58\uac00 \uacb9\uce58\ub294 \uacbd\uc6b0\ub294 \uc5c6\uc73c\uba70, \uc801\uc5b4\ub3c4 \ud55c \ubc88\uc740 \ubc15\ud14c\ub9ac\uc544\uac00 \ub9cc\ub09c\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ubc15\ud14c\ub9ac\uc544\uac00 \uac19\uc740 \uce78\uc5d0 \uac00\uc7a5 \ub9ce\uc774 \uc788\uc5c8\uc744 \ub54c, \uba87 \ub9c8\ub9ac\ub098 \uc788\uc5c8\ub294\uc9c0 \ucd9c\ub825\ud55c\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 \uadf8 \ub54c\uc758 \uc2dc\uac04\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"3116","problem_lang":"1","title":"MIKRO","description":"<p>In the national biology competition, Mirko won a brand new microscope and now spends his free time exploring the micro-world.&nbsp;<\/p>\r\n\r\n<p>In one of his experiments, Mirko is studying the movement of bacteria in a sample of water from the stream near his building. 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