시간 제한메모리 제한제출정답맞힌 사람정답 비율
5 초 256 MB3632117476132.577%

문제

제주 올레길 코스로 유명한 산책로가 있다. 산책로의 입구는 산책로에서 가장 서쪽에 위치하고 있다. 이 산책로는 단순 경로이며 수평 구간과 수직 구간으로만 구성되어 있어 모든 코너에서 90도 각도로 왼쪽 또는 오른쪽으로 회전만 할 수 있다. 또한 입구에서 출구 방향으로 걸어갈 때 동쪽에서 서쪽으로 이동을 전혀 하지 않아도, 즉, 보행자의 현재 위치를 나타내는 좌표의 x축 값이 작아지는 경우가 없이도 출구까지 도달할 수 있다. 그래서 이 산책로를 모노톤길이라고 부른다. 그림 1은 모노톤길의 예를 보여준다.

그림 1. 모노톤길의 예

이 산책로에는 n개의 카페가 곳곳에 들어서 있다. 특히 입구와 출구, 그리고 모든 코너에는 카페가 들어서 있다. 올레길 코스 관리자인 김씨는 이 산책로에 들어서 있는 모든 카페들의 위치 좌표를 가지고 있다. 입구 좌표는 항상 원점 (0,0) 이다. 그는 이들 카페에 1부터 n까지의 일렬 번호를 붙이려고 한다. 입구의 카페는 1번, 그 다음부터는 길을 따라가면서 만나는 순서대로 번호를 배정한다. 입구에서 출구로 갈 때, 카페 A를 카페 B보다 먼저 만나게 된다면, A에는 B보다 더 작은 번호를 배정한다. 따라서 그림 1의 산책로에서 좌표 (3,1)에 위치한 카페의 번호는 5이고, 좌표 (9,0)에 위치한 카페는 14번이고, 출구의 카페는 17번이다. 그는 산책로를 직접 걷지 않고 카페의 좌표들만으로 이 작업을 수행하고 싶어 한다. 그를 도와서 카페에 번호를 붙이는 작업을 수행하는 프로그램을 작성하시오.

입력

입력 데이터는 표준입력을 사용한다. 입력은 T개의 테스트 데이터로 구성된다. 입력의 첫 번째 줄에는 테스트 데이터의 개수 T가 정수로 주어진다. 각 테스트 데이터의 첫 번째 줄에는 카페의 수를 나타내는 정수 n (2 ≤ n ≤ 100,000)이 주어진다. 그 다음 n개의 줄에는 각 줄마다 각 카페의 좌표 (x,y)를 나타내는 두 개의 정수 x와 y가 주어진다. (0 ≤ x ≤ 100,000, -100,000 ≤ y ≤ 100,000). 입구 좌표는 항상 (0,0)이다. 어떤 두 카페도 동일한 좌표를 가지는 경우는 없다. 마지막 줄에는 정수 m (1 ≤ m ≤ 10)과 m개의 정수가 주어진다. m개의 각 정수는 1 이상 n 이하로서 카페의 번호를 나타낸다.

출력

출력은 표준출력을 사용한다. 각 테스트 데이터에 대해, 카페 번호로서 주어진 m개의 정수에 대한 답을 순서대로 한 줄에 하나씩 출력한다. 정수 k에 대한 답은 번호가 k인 카페의 좌표 (x,y)를 나타내는 두 개의 정수 x와 y이다.

예제 입력 1

2
17
3 3
5 3
11 2
9 2
2 1
3 1
5 1
0 0
1 0
2 0
9 0
11 -1
9 -3
6 -1
7 -1
7 -3
5 -1
3 5 14 17
4
0 0
0 1
1 1
1 0
5 1 4 1 3 1

예제 출력 1

3 1
9 0
11 -1
0 0
1 0
0 0
1 1
0 0
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(0 &le; x &le; 100,000, -100,000 &le; y &le; 100,000). \uc785\uad6c \uc88c\ud45c\ub294 \ud56d\uc0c1 (0,0)\uc774\ub2e4. \uc5b4\ub5a4 \ub450 \uce74\ud398\ub3c4 \ub3d9\uc77c\ud55c \uc88c\ud45c\ub97c \uac00\uc9c0\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4. \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 \uc815\uc218 m (1 &le; m &le; 10)\uacfc m\uac1c\uc758 \uc815\uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. m\uac1c\uc758 \uac01 \uc815\uc218\ub294 1 \uc774\uc0c1 n \uc774\ud558\ub85c\uc11c \uce74\ud398\uc758 \ubc88\ud638\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n","output":"<p>\ucd9c\ub825\uc740 \ud45c\uc900\ucd9c\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ub370\uc774\ud130\uc5d0 \ub300\ud574, \uce74\ud398 \ubc88\ud638\ub85c\uc11c \uc8fc\uc5b4\uc9c4 m\uac1c\uc758 \uc815\uc218\uc5d0 \ub300\ud55c \ub2f5\uc744 \uc21c\uc11c\ub300\ub85c \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud55c\ub2e4. \uc815\uc218 k\uc5d0 \ub300\ud55c \ub2f5\uc740 \ubc88\ud638\uac00 k\uc778 \uce74\ud398\uc758 \uc88c\ud45c (x,y)\ub97c \ub098\ud0c0\ub0b4\ub294 \ub450 \uac1c\uc758 \uc815\uc218 x\uc640 y\uc774\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"11067","problem_lang":"1","title":"Monotone Walkway","description":"<p>There is a famous walkway which is a Jeju Olle trail course. The entrance is one of the westernmost positions of this walkway. Since the walkway is a simple path which consists of horizontal sections and vertical sections, a walker should turn 90 degree left or right at every corner of the path. Also, a walker can move from the entrance to the exit without moving from east to west, i.e., without decreasing the x-coordinate of one&#39;s current position. So, this path is called a monotone walkway. Figure 1 shows an example of a monotone walkway<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/11067\/1.png\" style=\"height:188px; line-height:20.8px; text-align:center; width:321px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure 1. An example of a monotone walkway<\/p>\r\n\r\n<p>There are n caf&eacute;s along the walkway here and there. Specifically, there exist caf&eacute;s on the entrance, the exit, and all corners of the path. Mr. Kim, a manager of Jeju Olle trail courses, has the location coordinates of all caf&eacute;s. The coordinate of the entrance is always the origin (0,0). He is going to number all caf&eacute;s from 1 to n. The caf&eacute; located on the entrance is assigned the number 1. The remaining caf&eacute;s are assigned the numbers according to the order they are visited. Traversing the walkway from the entrance to the exit, a caf&eacute; A which is visited before another caf&eacute; B is assigned the smaller number than the caf&eacute; B. In the walkway of Figure 1, the caf&eacute;s located on the coordinates (3,1) and (9,0) are assigned the number 5 and 14, respectively, and the caf&eacute; on the exit is assigned the number 17. He wants to do his work without having to walk the path. To help him, you are to write a program which carries out the work of numbering the caf&eacute;s.<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with a line containing an integer, n (2 &le; n &le; 100,000), where n is the number of caf&eacute;s. In the following n lines, each coordinate of the n caf&eacute;s is given line by line. Each coordinate is represented by two numbers x and y, which are the x-coordinate and the y-coordinate of the caf&eacute;, respectively (0 &le; x &le; 100,000 and -100,000 &le; y &le; 100,000). The coordinate of the entrance is always (0,0). Note that there are no two caf&eacute;s which have a same coordinate. The last line of the input has an integer m (1 &le; m &le; 10) and m additional integers between 1 and n, inclusively, which are the caf&eacute; numbers.<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line for each of m integers given as caf&eacute; numbers in each test case. The line should contain two integers x and y representing the coordinate of the caf&eacute; whose number is k for a given integer k.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]