시간 제한메모리 제한제출정답맞힌 사람정답 비율
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문제

오래된 컴퓨터에서 그림판을 사용하고 있다. 그림판의 화면은 픽셀이라 부르는 칸을 가진 격자 모양이다. 가장 왼쪽 아래 픽셀의 좌표를 $(1, 1)$로 하고, 오른쪽으로 $a$번째 위쪽으로 $b$번째 픽셀의 좌표를 $(a, b)$로 한다. 초기 화면에는 수직, 수평 변을 가진  $N$개의 직사각형들이 그려져 있다. 직사각형은 이 구역안에 포함된 픽셀들로 표현된다. 

$N$개의 직사각형에 $M$개의 이동 명령이 수행될 것이다. 직사각형의 이동은 동, 서, 남, 북의 4방향과 북동, 북서, 남동, 남서(수평축과 45도 방향) 4방향으로 이루어진다. 또한 이동 거리 $d$가 주어진다. 다시 말해서, 이동 명령은 방향과 거리로 주어진다. 구체적으로, 직사각형의 가장 왼쪽, 아래 모서리 픽셀의 좌표가 $(a, b)$라 하면, 동, 북, 서, 남 방향으로 거리 $d$만큼의 이동은 모서리가 각각 $(a+d, b)$, $(a, b+d)$, $(a-d, b)$, $(a, b-d)$가 된다. 또한 북동, 북서, 남서, 남동 방향으로 거리 $d$만큼의 이동은 각각 $(a+d, b+d)$, $(a-d, b+d)$, $(a-d, b-d)$, $(a+d, b-d)$가 된다 (그림 1).

           

그림 1

화면에서 직사각형 $R$의 거리 $d$만큼 이동은 초기 위치를 포함해서 $R$이 거리 1 만큼 이동할 때마다 $R$의 모습을 순서대로 빠르게 나타냄으로서 구현된다. 하지만 우리의 컴퓨터는 아주 오래 되어서 $R$의 이동 시 렉이 심하게 걸린다. 결과적으로 $R$의 이동에서 그리게 되는 모든 $R$의 모습이 화면에 그대로 남아있게 된다. 따라서 $R$이 거리 $d$만큼 이동하면, $d$개의 직사각형들이 새롭게 화면에 만들어진다. 예를 들어, 아래 그림 2에서 직사각형이 북동방향으로 거리 3만큼 이동하면, 3개의 직사각형들이 만들어져서 총 4개의 직사각형이 화면 위에 남게 된다. 물론, 이동 후에는 북동 방향 끝에 있는 직사각형이 $R$ 이 된다.

그림 2

$M$개의 이동 명령을 수행한 후 $Q$개의 질의가 주어질 것이다. 각 질의는 평면 상의 픽셀 $p$로 주어진다. 질의에 대한 대답으로 픽셀 $p$를 포함하는 직사각형들의 개수를 출력한다.  

입력

첫째 줄에 공백으로 구분된 세 정수 $N$, $M$, $Q$가 주어진다.

다음 $N$개의 줄에는 공백으로 구분된 네 개의 정수 $x_1$, $y_1$, $x_2$, $y_2$가 주어지며, 직사각형의 가장 왼쪽 아래 픽셀의 좌표가 $(x_1, y_1)$, 가장 오른쪽 위 픽셀의 좌표가 $(x_2, y_2)$임을 의미한다. 직사각형은 $1$부터 $N$의 정수로 나타내며, $1$번 직사각형부터 순서대로 주어진다.

다음 $M$개의 줄에는 공백으로 구분된 세 개의 정수 $v_i$, $x_i$, $d_i$가 주어진다. $x_i$번째 직사각형이 $v_i$ 방향으로 $d_i$만큼 이동함을 나타낸다. $v_i$의 값은 다음과 같다.

  • 0: $(+1, 0)$
  • 1: $(+1, +1)$ 
  • 2: $(0, +1)$
  • 3: $(-1, +1)$ 
  • 4: $(-1, 0)$
  • 5: $(-1, -1)$ 
  • 6: $(0, -1)$
  • 7: $(+1, -1)$ 

다음 $Q$개의 줄에는 공백으로 구분된 두 정수 $x$, $y$가 주어지며, 질의에 해당하는 평면 상의 픽셀 $p$의 좌표 $(x, y)$를 나타낸다.

출력

각각의 질의마다 질의의 픽셀 $p$를 포함하는 직사각형들의 개수를 출력한다. $i$번째 줄에는 $i$번 질의의 결과를 출력해야 한다. ($0 ≤ i ≤ Q-1$)

제한

  • $1 \le N \le 250,000$
  • $0 \le M \le 250,000$
  • $1 \le Q \le 250,000$
  • $1 \le x_1 \le x_2 \le 250,000$
  • $1 \le y_1 \le y_2 \le 250,000$
  • $0 \le v_i \le 7$
  • $1 \le x_i \le N$
  • $1 \le d_i \le 250,000$
  • 화면의 좌표 값은 $1$이상 $250,000$이하이다. 임의의 직사각형에 포함되는 모든 픽셀들의 좌표값이 항상 이 범위안에 있다. 이는 이동이 일어난 이후에도 만족한다. 쿼리로 주어지는 픽셀 역시 이 조건을 만족한다.

서브태스크

번호배점제한
18

$N \le 100, M = 0$

28

$M = 0$

311

$M \le 100$

413

$v_i \in \{0, 2, 4, 6\}$ ($0 \le i \le M-1$). 즉, 직사각형은 상하좌우로만 움직인다.

512

$x_1 = x_2, y_1 = y_2$

648

추가적인 제약 조건이 없다.

예제 입력 1

1 8 3
2 1 2 1
0 1 1
1 1 1
2 1 1
3 1 1
4 1 1
5 1 1
6 1 1
7 1 1
1 1
2 1
4 2

예제 출력 1

0
2
1

예제 입력 2

2 0 3
3 3 7 7
4 4 6 6
5 5
3 7
8 8

예제 출력 2

2
1
0
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height: 291px;\" \/>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/0f8bb03a-bfcb-42f5-90d9-2c653c7b750b\/-\/preview\/\" style=\"width: 270px; height: 290px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\"><strong>\uadf8\ub9bc 1<\/strong><\/p>\r\n\r\n<p>\ud654\uba74\uc5d0\uc11c \uc9c1\uc0ac\uac01\ud615 $R$\uc758 \uac70\ub9ac $d$\ub9cc\ud07c \uc774\ub3d9\uc740 \ucd08\uae30 \uc704\uce58\ub97c \ud3ec\ud568\ud574\uc11c $R$\uc774 \uac70\ub9ac 1 \ub9cc\ud07c \uc774\ub3d9\ud560 \ub54c\ub9c8\ub2e4 $R$\uc758 \ubaa8\uc2b5\uc744 \uc21c\uc11c\ub300\ub85c \ube60\ub974\uac8c \ub098\ud0c0\ub0c4\uc73c\ub85c\uc11c \uad6c\ud604\ub41c\ub2e4. \ud558\uc9c0\ub9cc \uc6b0\ub9ac\uc758 \ucef4\ud4e8\ud130\ub294 \uc544\uc8fc \uc624\ub798 \ub418\uc5b4\uc11c $R$\uc758 \uc774\ub3d9 \uc2dc \ub809\uc774 \uc2ec\ud558\uac8c \uac78\ub9b0\ub2e4. \uacb0\uacfc\uc801\uc73c\ub85c $R$\uc758 \uc774\ub3d9\uc5d0\uc11c \uadf8\ub9ac\uac8c \ub418\ub294 \ubaa8\ub4e0 $R$\uc758 \ubaa8\uc2b5\uc774 \ud654\uba74\uc5d0 \uadf8\ub300\ub85c \ub0a8\uc544\uc788\uac8c \ub41c\ub2e4. \ub530\ub77c\uc11c $R$\uc774 \uac70\ub9ac $d$\ub9cc\ud07c \uc774\ub3d9\ud558\uba74, $d$\uac1c\uc758 \uc9c1\uc0ac\uac01\ud615\ub4e4\uc774 \uc0c8\ub86d\uac8c \ud654\uba74\uc5d0 \ub9cc\ub4e4\uc5b4\uc9c4\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc544\ub798 <strong>\uadf8\ub9bc 2<\/strong>\uc5d0\uc11c \uc9c1\uc0ac\uac01\ud615\uc774 \ubd81\ub3d9\ubc29\ud5a5\uc73c\ub85c \uac70\ub9ac 3\ub9cc\ud07c \uc774\ub3d9\ud558\uba74, 3\uac1c\uc758 \uc9c1\uc0ac\uac01\ud615\ub4e4\uc774 \ub9cc\ub4e4\uc5b4\uc838\uc11c \ucd1d 4\uac1c\uc758 \uc9c1\uc0ac\uac01\ud615\uc774 \ud654\uba74 \uc704\uc5d0 \ub0a8\uac8c \ub41c\ub2e4. \ubb3c\ub860, \uc774\ub3d9 \ud6c4\uc5d0\ub294 \ubd81\ub3d9 \ubc29\ud5a5 \ub05d\uc5d0 \uc788\ub294 \uc9c1\uc0ac\uac01\ud615\uc774 $R$ \uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/063e17e2-6bf0-477c-ab69-9b752c6edead\/-\/preview\/\" style=\"width: 140px; height: 158px;\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\"><strong>\uadf8\ub9bc 2<\/strong><\/p>\r\n\r\n<p>$M$\uac1c\uc758 \uc774\ub3d9 \uba85\ub839\uc744 \uc218\ud589\ud55c \ud6c4 $Q$\uac1c\uc758 \uc9c8\uc758\uac00 \uc8fc\uc5b4\uc9c8 \uac83\uc774\ub2e4. \uac01 \uc9c8\uc758\ub294 \ud3c9\uba74 \uc0c1\uc758 \ud53d\uc140 $p$\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uc9c8\uc758\uc5d0 \ub300\ud55c \ub300\ub2f5\uc73c\ub85c \ud53d\uc140 $p$\ub97c \ud3ec\ud568\ud558\ub294 \uc9c1\uc0ac\uac01\ud615\ub4e4\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. &nbsp;<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub41c \uc138 \uc815\uc218 $N$, $M$, $Q$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $N$\uac1c\uc758 \uc904\uc5d0\ub294 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub41c \ub124 \uac1c\uc758 \uc815\uc218&nbsp;$x_1$, $y_1$, $x_2$, $y_2$\uac00 \uc8fc\uc5b4\uc9c0\uba70, \uc9c1\uc0ac\uac01\ud615\uc758 \uac00\uc7a5 \uc67c\ucabd \uc544\ub798 \ud53d\uc140\uc758 \uc88c\ud45c\uac00&nbsp;$(x_1, y_1)$, \uac00\uc7a5 \uc624\ub978\ucabd \uc704 \ud53d\uc140\uc758 \uc88c\ud45c\uac00&nbsp;$(x_2, y_2)$\uc784\uc744 \uc758\ubbf8\ud55c\ub2e4. \uc9c1\uc0ac\uac01\ud615\uc740 $1$\ubd80\ud130 $N$\uc758 \uc815\uc218\ub85c \ub098\ud0c0\ub0b4\uba70, $1$\ubc88 \uc9c1\uc0ac\uac01\ud615\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c $M$\uac1c\uc758 \uc904\uc5d0\ub294 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub41c \uc138 \uac1c\uc758 \uc815\uc218&nbsp;$v_i$, $x_i$, $d_i$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \b$x_i$\ubc88\uc9f8 \uc9c1\uc0ac\uac01\ud615\uc774 $v_i$ \ubc29\ud5a5\uc73c\ub85c $d_i$\ub9cc\ud07c \uc774\ub3d9\ud568\uc744 \ub098\ud0c0\ub0b8\ub2e4. $v_i$\uc758 \uac12\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>0: $(+1, 0)$<\/li>\r\n\t<li>1: $(+1, +1)$&nbsp;<\/li>\r\n\t<li>2: $(0, +1)$<\/li>\r\n\t<li>3: $(-1, +1)$&nbsp;<\/li>\r\n\t<li>4: $(-1, 0)$<\/li>\r\n\t<li>5: $(-1, -1)$&nbsp;<\/li>\r\n\t<li>6: $(0, -1)$<\/li>\r\n\t<li>7: $(+1, -1)$&nbsp;<\/li>\r\n<\/ul>\r\n\r\n<p>\ub2e4\uc74c $Q$\uac1c\uc758 \uc904\uc5d0\ub294 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub41c \ub450 \uc815\uc218 $x$, $y$\uac00 \uc8fc\uc5b4\uc9c0\uba70, \uc9c8\uc758\uc5d0 \ud574\ub2f9\ud558\ub294 \ud3c9\uba74 \uc0c1\uc758 \ud53d\uc140 $p$\uc758 \uc88c\ud45c $(x, y)$\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \uc9c8\uc758\ub9c8\ub2e4 \uc9c8\uc758\uc758 \ud53d\uc140 $p$\ub97c \ud3ec\ud568\ud558\ub294 \uc9c1\uc0ac\uac01\ud615\ub4e4\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. $i$\ubc88\uc9f8 \uc904\uc5d0\ub294 $i$\ubc88 \uc9c8\uc758\uc758 \uacb0\uacfc\ub97c \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4. ($0 &le; i &le; Q-1$)<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1 \\le N \\le 250,000$<\/li>\r\n\t<li>$0 \\le M \\le 250,000$<\/li>\r\n\t<li>$1 \\le Q \\le 250,000$<\/li>\r\n\t<li>$1 \\le x_1 \\le x_2 \\le 250,000$<\/li>\r\n\t<li>$1 \\le y_1 \\le y_2 \\le 250,000$<\/li>\r\n\t<li>$0 \\le v_i \\le 7$<\/li>\r\n\t<li>$1 \\le x_i \\le N$<\/li>\r\n\t<li>$1 \\le d_i \\le 250,000$<\/li>\r\n\t<li>\ud654\uba74\uc758 \uc88c\ud45c \uac12\uc740 $1$\uc774\uc0c1 $250,000$\uc774\ud558\uc774\ub2e4. \uc784\uc758\uc758 \uc9c1\uc0ac\uac01\ud615\uc5d0 \ud3ec\ud568\ub418\ub294 \ubaa8\ub4e0 \ud53d\uc140\ub4e4\uc758 \uc88c\ud45c\uac12\uc774 \ud56d\uc0c1 \uc774 \ubc94\uc704\uc548\uc5d0 \uc788\ub2e4. \uc774\ub294 \uc774\ub3d9\uc774 \uc77c\uc5b4\ub09c \uc774\ud6c4\uc5d0\ub3c4 \ub9cc\uc871\ud55c\ub2e4. \ucffc\ub9ac\ub85c \uc8fc\uc5b4\uc9c0\ub294 \ud53d\uc140 \uc5ed\uc2dc \uc774 \uc870\uac74\uc744 \ub9cc\uc871\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 100, M = 0$<\/p>\r\n","subtask2":"<p>$M = 0$<\/p>\r\n","subtask3":"<p>$M \\le 100$<\/p>\r\n","subtask4":"<p>$v_i \\in \\{0, 2, 4, 6\\}$ ($0 \\le i \\le M-1$).&nbsp;\uc989, \uc9c1\uc0ac\uac01\ud615\uc740 \uc0c1\ud558\uc88c\uc6b0\ub85c\ub9cc \uc6c0\uc9c1\uc778\ub2e4.<\/p>\r\n","subtask5":"<p>$x_1 = x_2, y_1 = y_2$<\/p>\r\n","subtask6":"<p>\ucd94\uac00\uc801\uc778 \uc81c\uc57d \uc870\uac74\uc774 \uc5c6\ub2e4.<\/p>\r\n"},{"problem_id":"22028","problem_lang":"1","title":"Lag","description":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/a10050be-c8e6-430b-903f-efa621347ce3\/-\/preview\/\" style=\"width: 550px; height: 463px;\" \/><\/p>\r\n\r\n<p>You are using Paint on an old computer. The screen of Paint is a grid with cells called pixels. Let the coordinates of the lower-left pixel be $(1, 1)$, and the coordinates of the $a$th pixel from the left and the $b$th pixel from the bottom are $(a, b)$. On the initial screen, $N$ rectangles with vertical and horizontal sides are drawn. A rectangle is represented by pixels contained within this area.<\/p>\r\n\r\n<p>$M$ move commands will be performed on $N$ rectangles. The movement of the rectangle are represented by the pair of direction and distance. The directions are one of the following: east, west, south, north, northeast, northwest, southeast, and southwest (45 degrees to the horizontal axis). The distance is a positive integer $d$. Suppose that the original coordinates of the pixels of the leftmost and bottom corners of the rectangle are $(a, b)$. the movement by a distance of $d$ in the east, north, west, and south directions causes the rectangle to move toward the coordinate $(a+d, b)$, $(a, b+d)$, $(a-d, b)$, $(a, b-d)$. In addition, the movement by a distance of $d$ in the northeast, northwest, southwest, and southeast directions causes the rectangle to move toward the coordinate $(a+d, b+d)$, $(a-d, b+d)$, $(a-d, b-d)$, $(a+d, b-d)$&nbsp;<\/p>\r\n\r\n<p>Moving by distance $d$ of the rectangle $R$ on the screen is implemented by quickly displaying the shapes of $R$ every time when $R$ moves by distance 1. However, our computer is very old, so moving $R$ is very laggy. As a result, all of the $R$ drawn in the movement of $R$ remains on the screen. Therefore, if $R$ moves by the distance $d$, $d$ rectangles are newly created on the screen. For example, if the rectangle moves in the northeast direction by a distance of 3, 3 rectangles are created, leaving a total of 4 rectangles on the screen. Of course, after moving, the rectangle at the northeast end becomes $R$.<\/p>\r\n\r\n<p>After executing $M$ move commands, $Q$ queries will be given. Each query is given as a pixel $p$ on the plane. Print the number of rectangles containing the pixel $p$ as an answer to the query.<\/p>\r\n","input":"<p>The first line contains three space-separated integers $N, M, Q$.<\/p>\r\n\r\n<p>The next $N$ lines contain four space-separated integers $x_1, y_1, x_2, y_2$, denoting a rectangle with lowest-leftmost pixel $(x_1, y_1)$ and highest-rightmost pixel $(x_2, y_2)$.<\/p>\r\n\r\n<p>The next $M$ lines contain three space-separated integers $v_i, x_i, d_i$, denoting that the $x_i$-th rectangle moved toward the direction $v_i$ by distance $d_i$. The directions are:<\/p>\r\n\r\n<ul>\r\n\t<li>0: $(+1, 0)$<\/li>\r\n\t<li>1: $(+1, +1)$&nbsp;<\/li>\r\n\t<li>2: $(0, +1)$<\/li>\r\n\t<li>3: $(-1, +1)$&nbsp;<\/li>\r\n\t<li>4: $(-1, 0)$<\/li>\r\n\t<li>5: $(-1, -1)$&nbsp;<\/li>\r\n\t<li>6: $(0, -1)$<\/li>\r\n\t<li>7: $(+1, -1)$&nbsp;<\/li>\r\n<\/ul>\r\n\r\n<p>The next $Q$ lines contain two space-separated integers $x, y$, denoting the query on pixel $(x, y)$.<\/p>\r\n","output":"<p>For each query, print the single integer denoting the number of rectangles containing the given pixel.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1 \\le N \\le 250,000$<\/li>\r\n\t<li>$0 \\le M \\le 250,000$<\/li>\r\n\t<li>$1 \\le Q \\le 250,000$<\/li>\r\n\t<li>$1 \\le x_1 \\le x_2 \\le 250,000$<\/li>\r\n\t<li>$1 \\le y_1 \\le y_2 \\le 250,000$<\/li>\r\n\t<li>$0 \\le v_i \\le 7$<\/li>\r\n\t<li>$1 \\le x_i \\le N$<\/li>\r\n\t<li>$1 \\le d_i \\le 250,000$<\/li>\r\n\t<li>All coordinates are a positive integer from $1$ to $250\\,000$. Any pixels contained in a rectangle at any time satisfies this constraints. Queried pixels also satisfies this constraints.<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 100, M = 0$<\/p>\r\n","subtask2":"<p>$M = 0$<\/p>\r\n","subtask3":"<p>$M \\le 100$<\/p>\r\n","subtask4":"<p>$v_i \\in \\{0, 2, 4, 6\\}$ ($0 \\le i \\le M-1$).<\/p>\r\n","subtask5":"<p>$x_1 = x_2, y_1 = y_2$<\/p>\r\n","subtask6":"<p>No additional limits.<\/p>\r\n"}]

채점 및 기타 정보

  • 예제는 채점하지 않는다.
  • 이 문제의 채점 우선 순위는 2이다.