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문제

21XX년, 당신이 사는 행성은 큰 위기를 맞았고 행성의 대표인 당신은 FTL (Faster Than Light) 엔진을 이용하여 최근에 발견된 "BOJ-1014" 행성으로 사람들을 이주시킬 계획을 세우고 있다.

당신이 사는 행성에는 N개의 나라가 있으며 M개의 우호적 관계가 있고 "BOJ-1014" 행성에는 L (L ≥ N) 개의 거주지역이 있다. 거주지역은 2차원 좌표평면에 나타내었을 때 i번 거주 지역은 Pi(Xi, Yi) (1 ≤ i ≤ L) 에 있다. 각 거주지역에는 오직 한 나라만 들어설 수 있다.

어떤 두 나라가 우호적 관계에 있으면 그 두 나라를 잇는 철도를 건설해야 한다. 철도는 두 나라를 잇는 선분이며 한 철도가 다른 철도와 교차하는 상황이 발생할 수 있다. 철도가 서로 교차하는 점이 있을 때 위험할 수 있고 건설 비용도 더 많이 들어가므로 가능한 교차하는 철도의 쌍을 최소화 하고자 한다.

당신의 행성의 나라와 우호적 관계 그리고 이주할 행성의 정보가 주어졌을 때 나라들을 잘 배치하여 교차하는 철도의 쌍의 개수를 가능한 적게 만드는 프로그램을 작성하자.

입력

총 5개의 부분 문제로 구성되어 있으며 한 개의 부분문제는 한 개의 입력 데이터를 가진다. (밑의 힌트 부분을 참조)

입력 파일의 형식은 다음과 같다.

  • 첫 번째 줄에는 N과 M이 주어진다. N은 나라의 수를, M은 M개의 우호적 관계가 있음을 뜻한다.
  • 다음 j (1 ≤ j ≤ M) 번째 줄에 2개의 정수 Aj와 Bj가 주어지는데 이는 Aj번 나라와 Bj번 나라가 우호관계에 있음을 나타낸다.
  • 다음 줄에는 거주지역의 개수 L이 주어진다.
  • 다음 i (1 ≤ i ≤ L) 번째 줄에는 2개의 정수 Xi와 Y가 주어지는데 i번 거주지역 Pi(Xi, Yi) 의 위치를 나타낸다. 

모든 입력 데이터는 다음 조건을 만족한다.

  • 1 ≤ Aj ≤ N.
  • 1 ≤ Bj ≤ N.
  • 1 ≤ Xi ≤ 100 000.
  • 1 ≤ Yi ≤ 100 000.
  • 거주지역 Pi, Pj, Pk (1 ≤ i < j < k ≤ L) 는 하나의 선으로 이어질 수 없다.
  • 임의의 두 도시에 대해 철도를 통해 가는 방법이 항상 존재한다. 

출력

입력 파일에 대하여 출력 데이터를 제출하면 된다. 출력 데이터는 총 N줄로 구성되어 있고 k (1 ≤ k ≤ N) 번째 줄에는 k번 나라가 위치한 지역의 번호가 있어야 한다.

예제 입력 1

6 10
1 2
1 3
1 4
1 5
1 6
2 4
2 6
3 4
3 5
4 6
7
2 1
2 5
4 3
6 7
7 3
8 5
9 1

예제 출력 1

1
5
4
2
7
3

힌트

이 문제는 압축 파일의 01.txt로 채점을 합니다.

주의

나라를 배치하는 방법에 따라 한 점에서 2개 이상의 철도가 교차할 수 있다.

부분 문제

각 부분 문제에 대하여 N, M, L, S, T 값은 아래의 테이블을 참조하길 바란다. 여기서 S와 T는 점수 측정을 위한 값이다.

Subtask N M L S T
1 30 50 60 25 100
2 125 124 300 0 75
3 200 2000 400 110000 250000
4 250 350 250 400 2000
5 300 1600 500 72000 150000

점수 측정

이 문제는 출력 데이터를 제출하여 점수를 받을 수 있으며 총 5개의 부분 문제가 있다. 각 부분 문제는 한 개의 데이터 파일로 구성되어 있으며 제출 시 아래의 조건에 따라 점수를 받을 수 있다.

  • 만약 출력이 문제 조건에 만족하지 않는 경우, 0점을 받는다.
  • 만약 출력이 문제 조건을 만족하는 경우, 점수는 각 부분 점수에 대해 정해져 있는 S와 T에 따라 점수를 받을 수 있다. 출력 데이터에서 교차하는 철도 쌍의 개수를 C라고 하자.
    • T < C 이면 0점을 받는다.
    • S < C ≦ T 이면 \( \lfloor 1 + 19 \times (\frac{T-C}{T-S}) \rfloor \) 여기서 \( \lfloor x \rfloor \) 는 x보다 작거나 같은 정수 중에서 가장 큰 정수를 말한다.
    • C ≤ S 이면 20점을 받는다.

예제 입력과 출력

예제의 입력에선 총 7개의 거주지역이 있으며 아래의 그림과 같다. 

총 6개의 나라가 있으며 다음과 같이 배치하고자 한다.

  • 1번 나라를 1번 지역으로 배치한다.
  • 2번 나라를 5번 지역으로 배치한다.
  • 3번 나라를 4번 지역으로 배치한다.
  • 4번 나라를 2번 지역으로 배치한다.
  • 5번 나라를 7번 지역으로 배치한다.
  • 6번 나라를 3번 지역으로 배치한다.

그다음 우호관계에 따라 철도를 건설하면 아래의 그림과 같이 된다. 총 2개의 철도 쌍이 교차하는 것을 알 수 있다.

  • 거주지역 1번 (1번 나라가 배치된 곳) 과 거주지역 4번 (3번 나라가 배치된 곳) 을 잇는 철도와 거주지역 2번 (4번 나라가 배치된 곳) 과 거주지역 3번 (6번 나라가 배치된 곳) 잇는 철도가 교차한다.
  • 거주지역 1번 (1번 나라가 배치된 곳) 과 거주지역 4번 (3번 나라가 배치된 곳) 을 잇는 철도와 거주지역 2번 (4번 나라가 배치된 곳) 과 거주지역 5번 (2번 나라가 배치된 곳) 잇는 철도가 교차한다.
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(\ubc11\uc758&nbsp;\ud78c\ud2b8 \ubd80\ubd84\uc744&nbsp;\ucc38\uc870)<\/p>\r\n\r\n<p>\uc785\ub825&nbsp;\ud30c\uc77c\uc758 \ud615\uc2dd\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uccab&nbsp;\ubc88\uc9f8 \uc904\uc5d0\ub294 N\uacfc M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. N\uc740 \ub098\ub77c\uc758 \uc218\ub97c,&nbsp;M\uc740 M\uac1c\uc758 \uc6b0\ud638\uc801 \uad00\uacc4\uac00 \uc788\uc74c\uc744&nbsp;\ub73b\ud55c\ub2e4.<\/li>\r\n\t<li>\ub2e4\uc74c j&nbsp;(1 &le; j &le; M)&nbsp;\ubc88\uc9f8&nbsp;\uc904\uc5d0 2\uac1c\uc758 \uc815\uc218 A<sub>j<\/sub>\uc640&nbsp;B<sub>j<\/sub>\uac00 \uc8fc\uc5b4\uc9c0\ub294\ub370 \uc774\ub294 A<sub>j<\/sub>\ubc88&nbsp;\ub098\ub77c\uc640 B<sub>j<\/sub>\ubc88&nbsp;\ub098\ub77c\uac00 \uc6b0\ud638\uad00\uacc4\uc5d0 \uc788\uc74c\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/li>\r\n\t<li>\ub2e4\uc74c \uc904\uc5d0\ub294 \uac70\uc8fc\uc9c0\uc5ed\uc758 \uac1c\uc218 L\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/li>\r\n\t<li>\ub2e4\uc74c i (1 &le; i &le; L)&nbsp;\ubc88\uc9f8 \uc904\uc5d0\ub294 2\uac1c\uc758 \uc815\uc218&nbsp;X<sub>i<\/sub>\uc640 Y<sub>i&nbsp;<\/sub>\uac00 \uc8fc\uc5b4\uc9c0\ub294\ub370 i\ubc88&nbsp;\uac70\uc8fc\uc9c0\uc5ed P<sub>i<\/sub>(X<sub>i,&nbsp;<\/sub>Y<sub>i<\/sub>)&nbsp;\uc758 \uc704\uce58\ub97c \ub098\ud0c0\ub0b8\ub2e4.&nbsp;<\/li>\r\n<\/ul>\r\n\r\n<p>\ubaa8\ub4e0 \uc785\ub825 \ub370\uc774\ud130\ub294 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>1 &le; A<sub>j<\/sub>&nbsp;&le; N.<\/li>\r\n\t<li>1 &le; B<sub>j<\/sub>&nbsp;&le; N.<\/li>\r\n\t<li>1 &le; X<sub>i<\/sub>&nbsp;&le; 100 000.<\/li>\r\n\t<li>1 &le; Y<sub>i<\/sub>&nbsp;&le; 100 000.<\/li>\r\n\t<li>\uac70\uc8fc\uc9c0\uc5ed P<sub>i<\/sub>, P<sub>j<\/sub>, P<sub>k<\/sub>&nbsp;(1 &le; i &lt; j &lt; k &le; L)&nbsp;\ub294 \ud558\ub098\uc758 \uc120\uc73c\ub85c \uc774\uc5b4\uc9c8 \uc218 \uc5c6\ub2e4.<\/li>\r\n\t<li>\uc784\uc758\uc758 \ub450 \ub3c4\uc2dc\uc5d0 \ub300\ud574 \ucca0\ub3c4\ub97c \ud1b5\ud574 \uac00\ub294 \ubc29\ubc95\uc774 \ud56d\uc0c1 \uc874\uc7ac\ud55c\ub2e4.&nbsp;<\/li>\r\n<\/ul>\r\n","output":"<p>\uc785\ub825 \ud30c\uc77c\uc5d0 \ub300\ud558\uc5ec \ucd9c\ub825 \ub370\uc774\ud130\ub97c&nbsp;\uc81c\ucd9c\ud558\uba74 \ub41c\ub2e4. \ucd9c\ub825 \ub370\uc774\ud130\ub294&nbsp;\ucd1d N\uc904\ub85c \uad6c\uc131\ub418\uc5b4 \uc788\uace0 k (1 &le; k &le; N)&nbsp;\ubc88\uc9f8 \uc904\uc5d0\ub294 k\ubc88 \ub098\ub77c\uac00 \uc704\uce58\ud55c \uc9c0\uc5ed\uc758 \ubc88\ud638\uac00 \uc788\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc774 \ubb38\uc81c\ub294&nbsp;<a href=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/data\/11936.zip\">\uc555\ucd95 \ud30c\uc77c<\/a>\uc758 01.txt\ub85c \ucc44\uc810\uc744 \ud569\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uc8fc\uc758<\/p>\r\n\r\n<p>\ub098\ub77c\ub97c \ubc30\uce58\ud558\ub294 \ubc29\ubc95\uc5d0 \ub530\ub77c&nbsp;\ud55c&nbsp;\uc810\uc5d0\uc11c 2\uac1c \uc774\uc0c1\uc758 \ucca0\ub3c4\uac00 \uad50\ucc28\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ubd80\ubd84 \ubb38\uc81c<\/p>\r\n\r\n<p>\uac01 \ubd80\ubd84 \ubb38\uc81c\uc5d0 \ub300\ud558\uc5ec&nbsp;N, M, L, S, T \uac12\uc740 \uc544\ub798\uc758 \ud14c\uc774\ube14\uc744 \ucc38\uc870\ud558\uae38 \ubc14\ub780\ub2e4. \uc5ec\uae30\uc11c S\uc640 T\ub294 \uc810\uc218 \uce21\uc815\uc744 \uc704\ud55c \uac12\uc774\ub2e4.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:40%;\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>Subtask<\/th>\r\n\t\t\t<th>N<\/th>\r\n\t\t\t<th>M<\/th>\r\n\t\t\t<th>L<\/th>\r\n\t\t\t<th>S<\/th>\r\n\t\t\t<th>T<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>30<\/td>\r\n\t\t\t<td>50<\/td>\r\n\t\t\t<td>60<\/td>\r\n\t\t\t<td>25<\/td>\r\n\t\t\t<td>100<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>125<\/td>\r\n\t\t\t<td>124<\/td>\r\n\t\t\t<td>300<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>75<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>3<\/td>\r\n\t\t\t<td>200<\/td>\r\n\t\t\t<td>2000<\/td>\r\n\t\t\t<td>400<\/td>\r\n\t\t\t<td>110000<\/td>\r\n\t\t\t<td>250000<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>4<\/td>\r\n\t\t\t<td>250<\/td>\r\n\t\t\t<td>350<\/td>\r\n\t\t\t<td>250<\/td>\r\n\t\t\t<td>400<\/td>\r\n\t\t\t<td>2000<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>300<\/td>\r\n\t\t\t<td>1600<\/td>\r\n\t\t\t<td>500<\/td>\r\n\t\t\t<td>72000<\/td>\r\n\t\t\t<td>150000<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>\uc810\uc218 \uce21\uc815<\/p>\r\n\r\n<p>\uc774 \ubb38\uc81c\ub294 \ucd9c\ub825 \ub370\uc774\ud130\ub97c&nbsp;\uc81c\ucd9c\ud558\uc5ec&nbsp;\uc810\uc218\ub97c \ubc1b\uc744 \uc218 \uc788\uc73c\uba70 \ucd1d 5\uac1c\uc758 \ubd80\ubd84 \ubb38\uc81c\uac00 \uc788\ub2e4. \uac01 \ubd80\ubd84 \ubb38\uc81c\ub294 \ud55c&nbsp;\uac1c\uc758 \ub370\uc774\ud130 \ud30c\uc77c\ub85c \uad6c\uc131\ub418\uc5b4 \uc788\uc73c\uba70 \uc81c\ucd9c&nbsp;\uc2dc \uc544\ub798\uc758 \uc870\uac74\uc5d0 \ub530\ub77c \uc810\uc218\ub97c \ubc1b\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ub9cc\uc57d \ucd9c\ub825\uc774&nbsp;\ubb38\uc81c \uc870\uac74\uc5d0 \ub9cc\uc871\ud558\uc9c0&nbsp;\uc54a\ub294 \uacbd\uc6b0, 0\uc810\uc744 \ubc1b\ub294\ub2e4.<\/li>\r\n\t<li>\ub9cc\uc57d \ucd9c\ub825\uc774 \ubb38\uc81c \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \uacbd\uc6b0, \uc810\uc218\ub294 \uac01 \ubd80\ubd84 \uc810\uc218\uc5d0 \ub300\ud574 \uc815\ud574\uc838 \uc788\ub294 S\uc640 T\uc5d0 \ub530\ub77c \uc810\uc218\ub97c \ubc1b\uc744 \uc218 \uc788\ub2e4. \ucd9c\ub825 \ub370\uc774\ud130\uc5d0\uc11c \uad50\ucc28\ud558\ub294 \ucca0\ub3c4 \uc30d\uc758 \uac1c\uc218\ub97c C\ub77c\uace0 \ud558\uc790.\r\n\t<ul>\r\n\t\t<li>T &lt; C \uc774\uba74 0\uc810\uc744 \ubc1b\ub294\ub2e4.<\/li>\r\n\t\t<li>S &lt; C \u2266 T \uc774\uba74 \\( \\lfloor 1 + 19 \\times (\\frac{T-C}{T-S})&nbsp;\\rfloor&nbsp;\\)&nbsp;\uc5ec\uae30\uc11c&nbsp;\\(&nbsp;\\lfloor x \\rfloor \\)&nbsp;\ub294 x\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc815\uc218 \uc911\uc5d0\uc11c \uac00\uc7a5 \ud070 \uc815\uc218\ub97c \ub9d0\ud55c\ub2e4.<\/li>\r\n\t\t<li>C &le; S \uc774\uba74 20\uc810\uc744 \ubc1b\ub294\ub2e4.<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n\r\n<p>\uc608\uc81c \uc785\ub825\uacfc \ucd9c\ub825<\/p>\r\n\r\n<p>\uc608\uc81c\uc758 \uc785\ub825\uc5d0\uc120 \ucd1d 7\uac1c\uc758 \uac70\uc8fc\uc9c0\uc5ed\uc774 \uc788\uc73c\uba70 \uc544\ub798\uc758 \uadf8\ub9bc\uacfc \uac19\ub2e4.&nbsp;<\/p>\r\n\r\n<p><img src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/11936\/1.png\" style=\"height:223px; width:268px\" \/><\/p>\r\n\r\n<p>\ucd1d 6\uac1c\uc758 \ub098\ub77c\uac00 \uc788\uc73c\uba70&nbsp;\ub2e4\uc74c\uacfc \uac19\uc774 \ubc30\uce58\ud558\uace0\uc790 \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>1\ubc88 \ub098\ub77c\ub97c 1\ubc88&nbsp;\uc9c0\uc5ed\uc73c\ub85c \ubc30\uce58\ud55c\ub2e4.<\/li>\r\n\t<li>2\ubc88 \ub098\ub77c\ub97c 5\ubc88&nbsp;\uc9c0\uc5ed\uc73c\ub85c \ubc30\uce58\ud55c\ub2e4.<\/li>\r\n\t<li>3\ubc88 \ub098\ub77c\ub97c 4\ubc88&nbsp;\uc9c0\uc5ed\uc73c\ub85c \ubc30\uce58\ud55c\ub2e4.<\/li>\r\n\t<li>4\ubc88 \ub098\ub77c\ub97c 2\ubc88&nbsp;\uc9c0\uc5ed\uc73c\ub85c \ubc30\uce58\ud55c\ub2e4.<\/li>\r\n\t<li>5\ubc88 \ub098\ub77c\ub97c 7\ubc88&nbsp;\uc9c0\uc5ed\uc73c\ub85c \ubc30\uce58\ud55c\ub2e4.<\/li>\r\n\t<li>6\ubc88 \ub098\ub77c\ub97c 3\ubc88&nbsp;\uc9c0\uc5ed\uc73c\ub85c \ubc30\uce58\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uadf8\ub2e4\uc74c \uc6b0\ud638\uad00\uacc4\uc5d0 \ub530\ub77c \ucca0\ub3c4\ub97c \uac74\uc124\ud558\uba74 \uc544\ub798\uc758 \uadf8\ub9bc\uacfc \uac19\uc774 \ub41c\ub2e4. \ucd1d 2\uac1c\uc758 \ucca0\ub3c4&nbsp;\uc30d\uc774 \uad50\ucc28\ud558\ub294 \uac83\uc744&nbsp;\uc54c \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p><img src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/11936\/2.png\" style=\"height:229px; width:270px\" \/><\/p>\r\n\r\n<ul>\r\n\t<li>\uac70\uc8fc\uc9c0\uc5ed 1\ubc88 (1\ubc88 \ub098\ub77c\uac00 \ubc30\uce58\ub41c \uacf3) \uacfc \uac70\uc8fc\uc9c0\uc5ed 4\ubc88 (3\ubc88 \ub098\ub77c\uac00 \ubc30\uce58\ub41c \uacf3) \uc744 \uc787\ub294 \ucca0\ub3c4\uc640&nbsp;\uac70\uc8fc\uc9c0\uc5ed 2\ubc88 (4\ubc88 \ub098\ub77c\uac00 \ubc30\uce58\ub41c \uacf3) \uacfc \uac70\uc8fc\uc9c0\uc5ed 3\ubc88 (6\ubc88 \ub098\ub77c\uac00 \ubc30\uce58\ub41c \uacf3) \uc787\ub294 \ucca0\ub3c4\uac00 \uad50\ucc28\ud55c\ub2e4.<\/li>\r\n\t<li>\uac70\uc8fc\uc9c0\uc5ed 1\ubc88 (1\ubc88 \ub098\ub77c\uac00 \ubc30\uce58\ub41c \uacf3) \uacfc \uac70\uc8fc\uc9c0\uc5ed 4\ubc88 (3\ubc88 \ub098\ub77c\uac00 \ubc30\uce58\ub41c \uacf3) \uc744 \uc787\ub294 \ucca0\ub3c4\uc640&nbsp;\uac70\uc8fc\uc9c0\uc5ed 2\ubc88 (4\ubc88 \ub098\ub77c\uac00 \ubc30\uce58\ub41c \uacf3) \uacfc \uac70\uc8fc\uc9c0\uc5ed 5\ubc88 (2\ubc88 \ub098\ub77c\uac00 \ubc30\uce58\ub41c \uacf3) \uc787\ub294 \ucca0\ub3c4\uac00 \uad50\ucc28\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"11936","problem_lang":"1","title":"Project of Migration 1","description":"<p>In the year of 21XX, the JOI kingdom is faced with a big crisis. The King of the JOI kingdom takes the initiative to migrate people to the IOI star, which is a recently-discovered star.<\/p>\r\n\r\n<p>In the JOI kingdom, there are N ethnic groups numbered from 1 to N. There are M pairs of ethnic groups which have friendly relationships. On the IOI star, there are L resident areas numbered from 1 to L (L &ge; N). The resident area i is the point P<sub>i<\/sub>(X<sub>i<\/sub>, Y<sub>i<\/sub>) in the coordinate plane (1 &le; i &le; L). In the migration project, we allocate one of the resident areas to each ethnic group. No resident area is allocated to more than one ethnic groups.<\/p>\r\n\r\n<p>For each pair of ethnic groups having a friendly relationship, we will construct a railway track connecting their resident areas. A railway track is a line segment connecting two resident areas. It may happen that two railway tracks intersect each other depending on the way of allocation of resident areas.<\/p>\r\n\r\n<p>By request from the King, you are to find a migration project with minimum number of pairs of railway tracks intersecting each other.<\/p>\r\n\r\n<p>Given the information of ethnic groups in the JOI kingdom and the information of the resident areas on the IOI star, find a migration project with minimum number of pairs of railway tracks intersecting each other.<\/p>\r\n","input":"<p>There are five subtasks. Each subtask corresponds to a public input data file. The format of each input data file is as follows.<\/p>\r\n\r\n<ul>\r\n\t<li>The first line of input contains two space separated integers N and M. This means there are N ethnic groups in the JOI kingdom, and there are M pairs of ethnic groups having friendly relationships.<\/li>\r\n\t<li>The j-th line (1 &le; j &le; M) of the following M lines contains two space separated integers A<sub>j<\/sub> and B<sub>j<\/sub>. This means the ethnic group A<sub>j<\/sub> and the ethnic group B<sub>j<\/sub> have a friendly relationship.<\/li>\r\n\t<li>The following line contains an integer L, the number of resident areas on the IOI star.<\/li>\r\n\t<li>The i-th line (1 &le; i &le; L) of the following L lines contains two space separated integers X<sub>i<\/sub> and Y<sub>i<\/sub>. This means the resident area i is P<sub>i<\/sub>(X<sub>i<\/sub>, Y<sub>i<\/sub>) in the coordinate plane.<\/li>\r\n<\/ul>\r\n\r\n<p>All input data satisfy the following conditions.<\/p>\r\n\r\n<ul>\r\n\t<li>1 &le; A<sub>j<\/sub> &le; N.<\/li>\r\n\t<li>1 &le; B<sub>j<\/sub> &le; N.<\/li>\r\n\t<li>1 &le; X<sub>i<\/sub> &le; 100 000.<\/li>\r\n\t<li>1 &le; Y<sub>i<\/sub> &le; 100 000.<\/li>\r\n\t<li>P<sub>i<\/sub>, P<sub>j<\/sub>, P<sub>k<\/sub> do not lie in a line (1 &le; i &lt; j &lt; k &le; L).<\/li>\r\n\t<li>For any two ethnic groups, we can travel from the resident area of one group to the resident area of another group by passing through some railway tracks on the IOI star.<\/li>\r\n<\/ul>\r\n","output":"<p>For each input data file, submit an output data file. The output data file consists of N lines. The k-th line (1 &le; k &le; N) contains an integer which denotes the resident area allocated to the ethnic group k.<\/p>\r\n","hint":"<p>\uc774 \ubb38\uc81c\ub294 <a href=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/data\/11936.zip\">\uc555\ucd95 \ud30c\uc77c<\/a>\uc758 01.txt\ub85c \ucc44\uc810\uc744 \ud569\ub2c8\ub2e4.<\/p>\r\n\r\n<p>Note<\/p>\r\n\r\n<p>It may happen that more than two railway tracks intersect at a point depending on the way of allocation of resident areas.<\/p>\r\n\r\n<p>Subtasks<\/p>\r\n\r\n<p>For each subtask, the values of N, M, L, S, T are as in the following table. For the values of S, T, see Grading.<\/p>\r\n\r\n<table class=\"table table-bordered\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>Subtask<\/th>\r\n\t\t\t<th>N<\/th>\r\n\t\t\t<th>M<\/th>\r\n\t\t\t<th>L<\/th>\r\n\t\t\t<th>S<\/th>\r\n\t\t\t<th>T<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>30<\/td>\r\n\t\t\t<td>50<\/td>\r\n\t\t\t<td>60<\/td>\r\n\t\t\t<td>25<\/td>\r\n\t\t\t<td>100<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>125<\/td>\r\n\t\t\t<td>124<\/td>\r\n\t\t\t<td>300<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>75<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>3<\/td>\r\n\t\t\t<td>200<\/td>\r\n\t\t\t<td>2000<\/td>\r\n\t\t\t<td>400<\/td>\r\n\t\t\t<td>110000<\/td>\r\n\t\t\t<td>250000<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>4<\/td>\r\n\t\t\t<td>250<\/td>\r\n\t\t\t<td>350<\/td>\r\n\t\t\t<td>250<\/td>\r\n\t\t\t<td>400<\/td>\r\n\t\t\t<td>2000<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>300<\/td>\r\n\t\t\t<td>1600<\/td>\r\n\t\t\t<td>500<\/td>\r\n\t\t\t<td>72000<\/td>\r\n\t\t\t<td>150000<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>Grading<\/p>\r\n\r\n<p>This is an output-only task. There are five subtasks, and each subtask consists of one input data file. Submit an output data file for each subtask. Your score of each subtask is calculated as follows.<\/p>\r\n\r\n<ul>\r\n\t<li>If your migration project does not satisfy the conditions in the task statement, your score is 0.<\/li>\r\n\t<li>If your migration project satisfies the conditions in the task statement, your score is calculated according to the values of S, T as follows. Let C be the number of pairs of railway tracks intersecting each other.\r\n\t<ul>\r\n\t\t<li>If T &lt; C, your score is 0.<\/li>\r\n\t\t<li>If S &lt; C \u2266 T, your score is \\(\\lfloor 1 + 19 \\times \\left( \\frac {T-C}{T-S} \\right) \\rfloor\\). Here, \\(\\lfloor x\\rfloor\\) denotes the largest integer less than or equal to x.<\/li>\r\n\t\t<li>If C &le; S , your score is 20.<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n\r\n<p>Sample Input and Output<\/p>\r\n\r\n<p>In this sample input, there are seven resident areas on the IOI star as in the following figure.<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/11936\/1.png\" style=\"height:223px; width:268px\" \/><\/p>\r\n\r\n<p>There are six ethnic groups. We allocate a resident area to each ethnic group as follows.<\/p>\r\n\r\n<ul>\r\n\t<li>We allocate the resident area 1 to the ethnic group 1.<\/li>\r\n\t<li>We allocate the resident area 5 to the ethnic group 2.<\/li>\r\n\t<li>We allocate the resident area 4 to the ethnic group 3.<\/li>\r\n\t<li>We allocate the resident area 2 to the ethnic group 4.<\/li>\r\n\t<li>We allocate the resident area 7 to the ethnic group 5.<\/li>\r\n\t<li>We allocate the resident area 3 to the ethnic group 6.<\/li>\r\n<\/ul>\r\n\r\n<p>We will construct railway tracks as in the following figure. The number of pairs of railway tracks intersecting each other is 2.<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/11936\/2.png\" style=\"height:229px; width:270px\" \/><\/p>\r\n\r\n<ul>\r\n\t<li>The railway track connecting the resident area 1 (the place of the ethnic group 1) and the resident area 4 (the place of the ethnic group 3) and the railway track connecting the resident area 2 (the place of the ethnic group 4) and the resident area 3 (the place of the ethnic group 6) are intersecting each other.<\/li>\r\n\t<li>The railway track connecting the resident area 1 (the place of the ethnic group 1) and the resident area 4 (the place of the ethnic group 3) and the railway track connecting the resident area 2 (the place of the ethnic group 4) and the resident area 5 (the place of the ethnic group 2) are intersecting each other.<\/li>\r\n<\/ul>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

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Contest > JOI Open Contest > JOI Open Contest 2014 4-1번

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