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문제

상근이와 선영이는 장난감 동물을 가지고 재미있게 놀려고 한다. 먼저, 아래 세 가지 게임판 중 하나를 선택한다. 각 게임판은 여러 개의 칸(그림에는 동그라미)으로 이루어져 있고, 각 게임판은 일차원, 이차원, 삼차원 모양이다.

상근이는 N개의 작은 장난감 동물을 칸에 넣는다.

두 칸의 거리는 장난감 동물이 한 칸에서 출발해서 다른 칸으로 도착하는데 필요한 이동의 횟수이다. 장난감 동물은 자신이 있는 칸과 인접한 칸 중 하나로 이동할 수 있다. (각 칸과 인접한 칸은 그림에서 선분으로 이어져 있다)

두 장난감 동물이 서로의 소리를 들으려면 두 칸의 거리가 D보다 작거나 같아야 한다. 게임판의 종류와 각 장난감 동물의 위치, 그리고 D가 주어졌을 때, 서로의 소리를 들을 수 있는 장난감 동물의 쌍의 개수를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 네 정수 B, N, D, M이 주어진다.

B는 게임판의 종류이다. (1 ≤ B ≤ 3) 문제 설명의 왼쪽 그림이 1번 게임판, 중간 그림이 2번, 오른쪽 그림이 3번 게임판이다.

N은 장난감 동물의 수이다. (1 ≤ N ≤ 100,000)

D는 두 장난감 동물이 서로의 소리를 들을 수 있는 가장 먼 거리이다. (1 ≤ D ≤ 100,000,000)

M은 게임판의 크기이다. (입력으로 들어올 수 있는 가장 큰 좌표값) B가 1인 경우 M은 최대 75,000,000이고, 2인 경우에는 75,000, 3인 경우에는 75이다.

다음 N개의 줄에는 각 장난감 동물의 좌표가 주어진다. 모든 좌표는 1보다 크거나 같고, M보다 작거나 같은 자연수이다.

같은 칸에 장난감 동물 여러 개가 들어가 있을 수도 있다.

출력

첫째 줄에 서로의 소리를 들을 수 있는 장난감 동물의 쌍의 수를 출력한다.

예제 입력 1

2 5 4 10
5 2
7 2
8 4
6 5
4 4

예제 출력 1

8

힌트

1-2 (거리 2) 
1-4 (거리 4) 
1-5 (거리 3) 
2-3 (거리 3) 
2-4 (거리 4) 
3-4 (거리 3) 
3-5 (거리 4) 
4-5 (거리 3) 

[{"problem_id":"5476","problem_lang":"0","title":"\uc7a5\ub09c\uac10 \ub3d9\ubb3c","description":"<p>\uc0c1\uadfc\uc774\uc640 \uc120\uc601\uc774\ub294 \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc744 \uac00\uc9c0\uace0 \uc7ac\ubbf8\uc788\uac8c \ub180\ub824\uace0 \ud55c\ub2e4. \uba3c\uc800, \uc544\ub798 \uc138 \uac00\uc9c0 \uac8c\uc784\ud310 \uc911 \ud558\ub098\ub97c \uc120\ud0dd\ud55c\ub2e4. \uac01 \uac8c\uc784\ud310\uc740 \uc5ec\ub7ec \uac1c\uc758 \uce78(\uadf8\ub9bc\uc5d0\ub294 \ub3d9\uadf8\ub77c\ubbf8)\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \uac01 \uac8c\uc784\ud310\uc740 \uc77c\ucc28\uc6d0, \uc774\ucc28\uc6d0, \uc0bc\ucc28\uc6d0 \ubaa8\uc591\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/board.png\" style=\"height:138px; width:648px\" \/><\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 N\uac1c\uc758 \uc791\uc740 \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc744 \uce78\uc5d0 \ub123\ub294\ub2e4.<\/p>\r\n\r\n<p>\ub450 \uce78\uc758 \uac70\ub9ac\ub294 \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc774 \ud55c \uce78\uc5d0\uc11c \ucd9c\ubc1c\ud574\uc11c \ub2e4\ub978 \uce78\uc73c\ub85c \ub3c4\ucc29\ud558\ub294\ub370 \ud544\uc694\ud55c \uc774\ub3d9\uc758 \ud69f\uc218\uc774\ub2e4. \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc740 \uc790\uc2e0\uc774 \uc788\ub294 \uce78\uacfc \uc778\uc811\ud55c \uce78 \uc911 \ud558\ub098\ub85c \uc774\ub3d9\ud560 \uc218 \uc788\ub2e4. (\uac01 \uce78\uacfc \uc778\uc811\ud55c \uce78\uc740 \uadf8\ub9bc\uc5d0\uc11c \uc120\ubd84\uc73c\ub85c \uc774\uc5b4\uc838 \uc788\ub2e4)<\/p>\r\n\r\n<p>\ub450 \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc774 \uc11c\ub85c\uc758 \uc18c\ub9ac\ub97c \ub4e4\uc73c\ub824\uba74 \ub450 \uce78\uc758 \uac70\ub9ac\uac00 D\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc544\uc57c \ud55c\ub2e4. \uac8c\uc784\ud310\uc758 \uc885\ub958\uc640 \uac01 \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc758 \uc704\uce58, \uadf8\ub9ac\uace0 D\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c,&nbsp;\uc11c\ub85c\uc758 \uc18c\ub9ac\ub97c \ub4e4\uc744 \uc218 \uc788\ub294 \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc758 \uc30d\uc758 \uac1c\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub124 \uc815\uc218 B, N, D, M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>B\ub294 \uac8c\uc784\ud310\uc758 \uc885\ub958\uc774\ub2e4. (1 &le; B &le; 3) \ubb38\uc81c \uc124\uba85\uc758 \uc67c\ucabd \uadf8\ub9bc\uc774 1\ubc88 \uac8c\uc784\ud310, \uc911\uac04 \uadf8\ub9bc\uc774 2\ubc88, \uc624\ub978\ucabd \uadf8\ub9bc\uc774 3\ubc88 \uac8c\uc784\ud310\uc774\ub2e4.<\/p>\r\n\r\n<p>N\uc740 \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc758 \uc218\uc774\ub2e4. (1 &le; N &le; 100,000)<\/p>\r\n\r\n<p>D\ub294 \ub450 \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc774 \uc11c\ub85c\uc758 \uc18c\ub9ac\ub97c \ub4e4\uc744 \uc218 \uc788\ub294 \uac00\uc7a5 \uba3c \uac70\ub9ac\uc774\ub2e4. (1 &le; D &le; 100,000,000)<\/p>\r\n\r\n<p>M\uc740 \uac8c\uc784\ud310\uc758 \ud06c\uae30\uc774\ub2e4. (\uc785\ub825\uc73c\ub85c \ub4e4\uc5b4\uc62c \uc218 \uc788\ub294 \uac00\uc7a5 \ud070 \uc88c\ud45c\uac12) B\uac00 1\uc778 \uacbd\uc6b0 M\uc740 \ucd5c\ub300 75,000,000\uc774\uace0, 2\uc778 \uacbd\uc6b0\uc5d0\ub294 75,000, 3\uc778 \uacbd\uc6b0\uc5d0\ub294 75\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc758 \uc88c\ud45c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ubaa8\ub4e0 \uc88c\ud45c\ub294 1\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, M\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc790\uc5f0\uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>\uac19\uc740 \uce78\uc5d0 \uc7a5\ub09c\uac10 \ub3d9\ubb3c \uc5ec\ub7ec \uac1c\uac00 \ub4e4\uc5b4\uac00 \uc788\uc744 \uc218\ub3c4 \uc788\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc11c\ub85c\uc758 \uc18c\ub9ac\ub97c \ub4e4\uc744 \uc218 \uc788\ub294 \uc7a5\ub09c\uac10 \ub3d9\ubb3c\uc758 \uc30d\uc758 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>1-2 (\uac70\ub9ac 2)&nbsp;<br \/>\r\n1-4 (\uac70\ub9ac 4)&nbsp;<br \/>\r\n1-5 (\uac70\ub9ac 3)&nbsp;<br \/>\r\n2-3 (\uac70\ub9ac 3)&nbsp;<br \/>\r\n2-4 (\uac70\ub9ac 4)&nbsp;<br \/>\r\n3-4 (\uac70\ub9ac 3)&nbsp;<br \/>\r\n3-5 (\uac70\ub9ac 4)&nbsp;<br \/>\r\n4-5 (\uac70\ub9ac 3)&nbsp;<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5476","problem_lang":"1","title":"PAIRS","description":"<p>Mirko and Slavko are playing with toy animals. First, they choose one of three boards given in the figure below. Each board consists of cells (shown as circles in the figure) arranged into a one, two or three dimensional grid.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/board.png\" style=\"height:138px; width:648px\" \/><\/p>\r\n\r\n<p>Mirko then places N little toy animals into the cells.&nbsp;<\/p>\r\n\r\n<p>The distance between two cells is the smallest number of moves that an animal would need in order to reach one cell from the other. In one move, the animal may step into one of the adjacent cells (connected by line segments in the figure).&nbsp;<\/p>\r\n\r\n<p>Two animals can hear each other if the distance between their cells is at most D. Slavko&#39;s task is to calculate how many pairs of animals there are such that one animal can hear the other.<\/p>\r\n\r\n<p>Write a program that, given the board type, the locations of all animals, and the number D, finds the desired number of pairs.&nbsp;<\/p>\r\n","input":"<p>The first line of input contains four integers in this order:&nbsp;<\/p>\r\n\r\n<ul>\r\n\t<li>The board type B (1 &le; B &le; 3);&nbsp;<\/li>\r\n\t<li>The number of animals N (1 &le; N &le; 100 000);&nbsp;<\/li>\r\n\t<li>The largest distance D at which two animals can hear each other (1 &le; D &le; 100 000 000);&nbsp;<\/li>\r\n\t<li>The size of the board M (the largest coordinate allowed to appear in the input):&nbsp;\r\n\t<ul>\r\n\t\t<li>When B=1, M will be at most 75 000 000.&nbsp;<\/li>\r\n\t\t<li>When B=2, M will be at most 75 000.&nbsp;<\/li>\r\n\t\t<li>When B=3, M will be at most 75.&nbsp;<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n\r\n<p>Each of the following N lines contains B integers separated by single spaces, the coordinates of one toy animal.&nbsp;<\/p>\r\n\r\n<p>Each coordinate will be between 1 and M (inclusive).&nbsp;<\/p>\r\n\r\n<p>More than one animal may occupy the same cell.&nbsp;<\/p>\r\n","output":"<p>Output should consist of a single integer, the number of pairs of animals that can hear each other.&nbsp;<\/p>\r\n\r\n<p>Note: use a 64-bit integer type to calculate and output the result (long long in C\/C++, int64 in Pascal).&nbsp;<\/p>\r\n","hint":"<p>The eight pairs are:&nbsp;<\/p>\r\n\r\n<ul>\r\n\t<li>1-2 (distance 2)&nbsp;<\/li>\r\n\t<li>1-4 (distance 4)&nbsp;<\/li>\r\n\t<li>1-5 (distance 3)&nbsp;<\/li>\r\n\t<li>2-3 (distance 3)&nbsp;<\/li>\r\n\t<li>2-4 (distance 4)&nbsp;<\/li>\r\n\t<li>3-4 (distance 3)&nbsp;<\/li>\r\n\t<li>3-5 (distance 4)&nbsp;<\/li>\r\n\t<li>4-5 (distance 3)&nbsp;<\/li>\r\n<\/ul>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > International Olympiad in Informatics > IOI 2007 5번