시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 139 25 20 30.769%

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

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

예제 출력 1

3 
4
[{"problem_id":"3116","problem_lang":"0","title":"\uc0dd\ubb3c\ud559\uc790","description":"<p>\r\n\t\uc0dd\ubb3c\ud559\uc790\ub97c \uafc8\uafb8\ub294 \uac15\uc0b0\uc774\ub294 \uc0c8\ud574 \uc120\ubb3c\ub85c \ud604\ubbf8\uacbd\uc744 \ubc1b\uc558\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\r\n\t\uc5b4\ub290 \ub0a0, \ubb3c \uc18d\uc5d0 \uc788\ub294 \ubc15\ud14c\ub9ac\uc544\uc758 \uc6c0\uc9c1\uc784\uc744 \uad00\ucc30\ud558\uace0 \uc788\uc5c8\ub2e4. \uad00\ucc30\uc744 \ud55c \uc2dc\uac04 \uc815\ub3c4 \ud558\ub2e4\ubcf4\ub2c8, \uc77c\uc815\ud55c \uaddc\uce59\ub300\ub85c \uc6c0\uc9c1\uc778\ub2e4\ub294 \uac83\uc744 \uc54c \uc218 \uc788\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ubb3c\ubc29\uc6b8\uc740 \ud06c\uae30\uac00 \ubb34\ud55c\ub300\uc778 \uc815\uc0ac\uac01\ud615 \uaca9\uc790\ub85c \ubaa8\ub378\ub9c1 \ud560 \uc218 \uc788\ub2e4. \ubc15\ud14c\ub9ac\uc544\ub294 \ud55c \uc815\uc0ac\uac01\ud615\uc5d0 \uc788\ub2e4. \ubc15\ud14c\ub9ac\uc544\uac00 \uc6c0\uc9c1\uc774\ub294 \ubc29\ud5a5\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc22b\uc790\ub85c \ud45c\ud604\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n\r\n<table class=\"table table-bordered\" style=\"width: 12%;\">\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td style=\"width: 4%; text-align:center;\">\r\n\t\t\t\t1<\/td>\r\n\t\t\t<td style=\"width: 4%; text-align:center;\">\r\n\t\t\t\t2<\/td>\r\n\t\t\t<td style=\"width: 4%; text-align:center;\">\r\n\t\t\t\t3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td style=\"text-align:center;\">\r\n\t\t\t\t8<\/td>\r\n\t\t\t<td style=\"text-align:center;\">\r\n\t\t\t\tB<\/td>\r\n\t\t\t<td style=\"text-align:center;\">\r\n\t\t\t\t4<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td style=\"text-align:center;\">\r\n\t\t\t\t7<\/td>\r\n\t\t\t<td style=\"text-align:center;\">\r\n\t\t\t\t6<\/td>\r\n\t\t\t<td style=\"text-align:center;\">\r\n\t\t\t\t5<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>\r\n\t\ubaa8\ub4e0 \ubc15\ud14c\ub9ac\uc544\ub294 \ub3d9\uc2dc\uc5d0 \uc6c0\uc9c1\uc774\uace0, 1\ucd08 \ub2e8\uc704\ub85c \uc6c0\uc9c1\uc774\uace0, \ud55c \ubc29\ud5a5\uc73c\ub85c\ub9cc \uc6c0\uc9c1\uc778\ub2e4. \ubc15\ud14c\ub9ac\uc544 \uc5ec\ub7ec \ub9c8\ub9ac\uac00 \uac19\uc740 \uce78\uc5d0 \uc788\uc744 \uc218\ub3c4 \uc788\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ubc15\ud14c\ub9ac\uc544\uc758 \uc704\uce58\uc640 \uc6c0\uc9c1\uc774\ub294 \ubc29\ud5a5\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ubc15\ud14c\ub9ac\uc544 \uc5ec\ub7ec \ub9c8\ub9ac\uac00 \uac19\uc740 \uce78\uc5d0 \uc81c\uc77c \ub9ce\uc774 \uc788\uc744 \ub54c\uac00 \uc5b8\uc81c\uc778\uc9c0, \uadf8\ub9ac\uace0 \uadf8 \ub54c \uba87 \ub9c8\ub9ac\uac00 \uac19\uc740 \uce78\uc5d0 \uc788\uc5c8\ub294\uc9c0 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \ub9cc\uc57d \uc774\ub7ec\ud55c \ucd5c\ub313\uac12\uc774 \uc5ec\ub7ec\uac1c\ub77c\uba74, \uac00\uc7a5 \ube60\ub978 \uc2dc\uac04\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n","input":"<p>\r\n\t\uccab\uc9f8 \uc904\uc5d0 \ubc15\ud14c\ub9ac\uc544\uc758 \uc218 N(1 &le; N &le; 5,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.\ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0\ub294 \uc138 \uac1c\uc758 \uc815\uc218 X, Y, D (-1,000,000 &le; X,Y &le; 1,000,000), (1 &le; D &le; 8) \uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\r\n\tX\uc640 Y\ub294 \ubc15\ud14c\ub9ac\uc544\uc758 \uc2dc\uc791 \uc88c\ud45c\uc774\uba70, D\ub294 \ubc29\ud5a5\uc774\ub2e4. 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>\r\n\t\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\r\n\r\n","output":"<p>\r\n\t\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\r\n","hint":"","original":"0","html_title":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"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. He noticed that bacteria move in a very specific way.&nbsp;<\/p>\r\n\r\n<p>A drop of water can be modelled by an infinite square grid. For each bacterium, we know the coordinates of the unit square it is in and the direction it is moving in. The direction is a number between 1 and 8 as in the figure below.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/mikro.png\" style=\"height:102px; width:148px\" \/><\/p>\r\n\r\n<p>All bacteria move at the same time, at discrete time points, each in its own direction. Sometimes multiple bacteria find themselves in the same square. We say that a meeting of rank K took place at time T if some K bacteria found themselves in the same square exactly T moves after the beginning of the experiment.&nbsp;<\/p>\r\n\r\n<p>Mirko is intrigued by meetings of high rank so he wants to predict which meeting will have the highest rank and when it will happen. If there will be multiple such meetings of the highest rank, he is interested only in the time of the first meeting.&nbsp;<\/p>\r\n","input":"<p>The first line contains an integer N (1 &le; N &le; 5000), the number of bacteria. Each of the following N lines contains three integers X, Y and D (-1 000 000 &le; X, Y &le; 1 000 000), (1 &le; D &le; 8), the starting coordinates and direction of one bacteria. X-coordinates increase from left to right, y-coordinates increase upwards.&nbsp;<\/p>\r\n\r\n<p>No two bacteria will initially share the same coordinates.&nbsp;<\/p>\r\n\r\n<p>The input will guarantee that at least one meeting will occur.&nbsp;<\/p>\r\n","output":"<p>On the first line, output the highest rank of all meetings.&nbsp;<\/p>\r\n\r\n<p>On the second line, output the time of the first meeting of this highest rank.&nbsp;<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_code":"\uc601\uc5b4"}]