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문제

세계의 경제는 석유에 의존하고, 그것이 아직 남아있는 석유를 찾고 시추하는 방법을 개발하는 이유다. 정유회사의 수익은 얼마나 효율적으로 땅을 파야하는지에 달려있다. The International Crude Petroleum Consortium(ICPC)는 폭넓은 컴퓨터 시뮬레이션을 이용하여 얼마나 기름을 가능한 한 좋게 시추 할 수 있나 결정하려 한다.

새로 발견되는 석유는 하나로 뭉쳐있지 않고, 여러 갈래로 나뉘어져 있기 때문에 석유를 시추하는건 날이 가면 갈수록 어려워진다. ICPC는 현재 그림 G.1. 처럼 땅에 있는 석유 단층을 다루고 있다.

그림 G.1 : 땅에 뭍혀있는 석유 단층이다. 예제 입력 1과 같은 그림이다.

간단하게 분석하면, ICPC는 오직 석유 매장량과 평면만을 고려하여 지구 표면과 수평인 선분들을 그린다. ICPC는 하나의 시추 드릴에서 가장 최대의 석유를 뽑아내고 싶어한다. 석유는 지면으로부터 직선으로 시추되고, 드릴과 석유의 모든 교차점에서 시추가 가능하다. 심지어 석유층의 끝과 드릴이 닿아도 시추가 가능하다. 

한가지 예가 그림G.1과 같이 3개의 단층과 맞닿았다. 석유의 양은 좌우 넓이와 일치한다. 당신은 ICPC 가 하나의 시추드릴로 가장 많은 양의 석유를 시추할 수 있게 도와줄 수 있는가?

입력

입력의 첫 줄에는 석유층의 갯수인 정수 n (1 ≤ n ≤ 2 000) 이 입력된다.

다음 n개의 라인에는 각각의 석유 위치가 오게 되는데 각 줄은 3가지 정수 x0, x1 그리고  y 를 입력받게 된다. 석유위치는 (x0, y) 부터 (x1, y) 까지 위치하게 된다.

각 x0, x1 ,y는 |x0|, |x1| ≤ 10^6,  1 ≤ y ≤ 10^6 을 만족하며 석유는 서로 만나지 않으며 석유층의 끝끼리도 마주치지 않는다.

출력

하나의 시추드릴로 뽑을수 있는 최대 석유양을 출력하시오.

예제 입력 1

5
100 180 20
30 60 30
70 110 40
10 40 50
0 80 70

예제 출력 1

200

예제 입력 2

3
50 60 10
-42 -42 20
25 0 10

예제 출력 2

25
[{"problem_id":"12771","problem_lang":"0","title":"\uc11d\uc720","description":"<p>\uc138\uacc4\uc758 \uacbd\uc81c\ub294 \uc11d\uc720\uc5d0 \uc758\uc874\ud558\uace0, \uadf8\uac83\uc774 \uc544\uc9c1 \ub0a8\uc544\uc788\ub294 \uc11d\uc720\ub97c&nbsp;\ucc3e\uace0 \uc2dc\ucd94\ud558\ub294 \ubc29\ubc95\uc744 \uac1c\ubc1c\ud558\ub294 \uc774\uc720\ub2e4. \uc815\uc720\ud68c\uc0ac\uc758 \uc218\uc775\uc740&nbsp;\uc5bc\ub9c8\ub098 \ud6a8\uc728\uc801\uc73c\ub85c \ub545\uc744 \ud30c\uc57c\ud558\ub294\uc9c0\uc5d0 \ub2ec\ub824\uc788\ub2e4.&nbsp;The International Crude Petroleum Consortium(ICPC)\ub294 \ud3ed\ub113\uc740&nbsp;\ucef4\ud4e8\ud130 \uc2dc\ubbac\ub808\uc774\uc158\uc744 \uc774\uc6a9\ud558\uc5ec \uc5bc\ub9c8\ub098 \uae30\ub984\uc744 \uac00\ub2a5\ud55c \ud55c \uc88b\uac8c \uc2dc\ucd94 \ud560 \uc218 \uc788\ub098 \uacb0\uc815\ud558\ub824 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc0c8\ub85c \ubc1c\uacac\ub418\ub294 \uc11d\uc720\ub294&nbsp;\ud558\ub098\ub85c \ubb49\uccd0\uc788\uc9c0 \uc54a\uace0, \uc5ec\ub7ec \uac08\ub798\ub85c \ub098\ub258\uc5b4\uc838 \uc788\uae30 \ub54c\ubb38\uc5d0 \uc11d\uc720\ub97c&nbsp;\uc2dc\ucd94\ud558\ub294\uac74 \ub0a0\uc774 \uac00\uba74 \uac08\uc218\ub85d \uc5b4\ub824\uc6cc\uc9c4\ub2e4. ICPC\ub294 \ud604\uc7ac \uadf8\ub9bc G.1. \ucc98\ub7fc \ub545\uc5d0 \uc788\ub294 \uc11d\uc720&nbsp;\ub2e8\uce35\uc744 \ub2e4\ub8e8\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/12771\/1.png\" style=\"height:269px; text-align:center; width:547px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">\uadf8\ub9bc G.1 : \ub545\uc5d0&nbsp;\ubb4d\ud600\uc788\ub294 \uc11d\uc720&nbsp;\ub2e8\uce35\uc774\ub2e4. \uc608\uc81c \uc785\ub825 1\uacfc \uac19\uc740 \uadf8\ub9bc\uc774\ub2e4.<\/p>\r\n\r\n<p>\uac04\ub2e8\ud558\uac8c \ubd84\uc11d\ud558\uba74, ICPC\ub294 \uc624\uc9c1&nbsp;\uc11d\uc720 \ub9e4\uc7a5\ub7c9\uacfc&nbsp;\ud3c9\uba74\ub9cc\uc744&nbsp;\uace0\ub824\ud558\uc5ec&nbsp;\uc9c0\uad6c \ud45c\uba74\uacfc \uc218\ud3c9\uc778 \uc120\ubd84\ub4e4\uc744 \uadf8\ub9b0\ub2e4. ICPC\ub294 \ud558\ub098\uc758 \uc2dc\ucd94 \ub4dc\ub9b4\uc5d0\uc11c \uac00\uc7a5 \ucd5c\ub300\uc758 \uc11d\uc720\ub97c \ubf51\uc544\ub0b4\uace0 \uc2f6\uc5b4\ud55c\ub2e4. \uc11d\uc720\ub294&nbsp;\uc9c0\uba74\uc73c\ub85c\ubd80\ud130 \uc9c1\uc120\uc73c\ub85c \uc2dc\ucd94\ub418\uace0, \ub4dc\ub9b4\uacfc \uc11d\uc720\uc758 \ubaa8\ub4e0&nbsp;\uad50\ucc28\uc810\uc5d0\uc11c \uc2dc\ucd94\uac00 \uac00\ub2a5\ud558\ub2e4. \uc2ec\uc9c0\uc5b4 \uc11d\uc720\uce35\uc758 \ub05d\uacfc \ub4dc\ub9b4\uc774 \ub2ff\uc544\ub3c4 \uc2dc\ucd94\uac00 \uac00\ub2a5\ud558\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ud55c\uac00\uc9c0&nbsp;\uc608\uac00&nbsp;\uadf8\ub9bcG.1\uacfc \uac19\uc774&nbsp;3\uac1c\uc758 \ub2e8\uce35\uacfc \ub9de\ub2ff\uc558\ub2e4. \uc11d\uc720\uc758 \uc591\uc740 \uc88c\uc6b0 \ub113\uc774\uc640 \uc77c\uce58\ud55c\ub2e4. \ub2f9\uc2e0\uc740 ICPC \uac00 \ud558\ub098\uc758 \uc2dc\ucd94\ub4dc\ub9b4\ub85c \uac00\uc7a5 \ub9ce\uc740 \uc591\uc758 \uc11d\uc720\ub97c \uc2dc\ucd94\ud560 \uc218 \uc788\uac8c \ub3c4\uc640\uc904&nbsp;\uc218 \uc788\ub294\uac00?<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uccab \uc904\uc5d0\ub294 \uc11d\uc720\uce35\uc758 \uac2f\uc218\uc778 \uc815\uc218 n&nbsp;(1 &le; n &le; 2 000) \uc774 \uc785\ub825\ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c n\uac1c\uc758 \ub77c\uc778\uc5d0\ub294 \uac01\uac01\uc758 \uc11d\uc720 \uc704\uce58\uac00 \uc624\uac8c \ub418\ub294\ub370 \uac01 \uc904\uc740&nbsp;3\uac00\uc9c0 \uc815\uc218&nbsp;x0, x1 \uadf8\ub9ac\uace0&nbsp;&nbsp;y \ub97c \uc785\ub825\ubc1b\uac8c \ub41c\ub2e4. \uc11d\uc720\uc704\uce58\ub294&nbsp;(x0, y) \ubd80\ud130&nbsp;(x1, y) \uae4c\uc9c0 \uc704\uce58\ud558\uac8c&nbsp;\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uac01 x0, x1 ,y\ub294 |x0|, |x1| &le; 10^6,&nbsp;&nbsp;1 &le; y &le; 10^6 \uc744 \ub9cc\uc871\ud558\uba70 \uc11d\uc720\ub294 \uc11c\ub85c \ub9cc\ub098\uc9c0 \uc54a\uc73c\uba70 \uc11d\uc720\uce35\uc758 \ub05d\ub07c\ub9ac\ub3c4 \ub9c8\uc8fc\uce58\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","output":"<p>\ud558\ub098\uc758 \uc2dc\ucd94\ub4dc\ub9b4\ub85c \ubf51\uc744\uc218 \uc788\ub294 \ucd5c\ub300 \uc11d\uc720\uc591\uc744 \ucd9c\ub825\ud558\uc2dc\uc624.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"12771","problem_lang":"1","title":"Oil","description":"<p>A large part of the world economy depends on oil, which is why research into new methods for finding and extracting oil is still active. Profits of oil companies depend in part on how efficiently they can drill for oil. The International Crude Petroleum Consortium (ICPC) hopes that extensive computer simulations will make it easier to determine how to drill oil wells in the best possible way.<\/p>\r\n\r\n<p>Drilling oil wells optimally is getting harder each day &ndash; the newly discovered oil deposits often do not form a single body, but are split into many parts. The ICPC is currently concerned with stratified deposits, as illustrated in Figure G.1.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/12771\/1.png\" style=\"height:269px; width:547px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure G.1: Oil layers buried in the earth. This figure corresponds to Sample Input 1.<\/p>\r\n\r\n<p>To simplify its analysis, the ICPC considers only the 2-dimensional case, where oil deposits are modeled as horizontal line segments parallel to the earth&rsquo;s surface. The ICPC wants to know how to place a single oil well to extract the maximum amount of oil. The oil well is drilled from the surface along a straight line and can extract oil from all deposits that it intersects on its way down, even if the intersection is at an endpoint of a deposit. One such well is shown as a dashed line in Figure G.1, hitting three deposits. In this simple model the amount of oil contained in a deposit is equal to the width of the deposit. Can you help the ICPC determine the maximum amount of oil that can be extracted by a single well?<\/p>\r\n","input":"<p>The first line of input contains a single integer n (1 &le; n &le; 2 000), which is the number of oil deposits. This is followed by n lines, each describing a single deposit. These lines contain three integers x<sub>0<\/sub>, x<sub>1<\/sub>, and y giving the deposit&rsquo;s position as the line segment with endpoints (x<sub>0<\/sub>, y) and (x<sub>1<\/sub>, y). These numbers satisfy |x<sub>0<\/sub>|, |x<sub>1<\/sub>| &le; 10<sup>6<\/sup> and 1 &le; y &le; 10<sup>6<\/sup>. No two deposits will intersect, not even at a point.<\/p>\r\n","output":"<p>Display the maximum amount of oil that can be extracted by a single oil well.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > World Finals > 2016 World Finals G번