시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 38 10 4 40.000%

문제

일요일을 맞이해 창영이는 집안의 모든 침대 시트를 빨고, 집 앞 잔디밭에서 말리고 있다. 갑자기, 엄청난 강풍이 몰아쳤고 모든 침대 시트는 땅바닥에 떨어지게 되었다.

잔디밭은 크기가 무한대인 정사각형 격자로 나타낼 수 있고, 각 단위 정사각형은 좌표 쌍으로 나타낼 수 있다. 침대 시트는 직사각형이며, 축에 평행하다. 시트는 서로 겹칠 수도 있다.

다시 빨래줄에 시트를 걸어놓기 위해 창영이는 막대를 (0,0)에 꽂았다. 그런데 갑자기 땅에서 기름이 나오기 시작했다. 창영이는 이런 예상하지 못한 상황에 당황하였고 결국 기절했다. 창영이가 기절한 사이에 기름은 퍼져나갔다.

시간은 기름이 퍼지기 시작한 순간부터 측정하기 시작한다. 가장 처음에는 단위 정사각형 (0,0)만 기름이 있다. 기름은 아래 그림에 나와있는 것 같이 1초에 한 정사각형씩 여덟 방향으로 이동한다. 기름이 단위 정사각형에 들어가게 되면, 즉시 그 정사각형을 가득 채우게 되고, 그 부분에 속해있는 시트에도 기름이 스며들게 된다.

시간 0, 1, 2초의 모습이다.

입력으로 주어지는 시간이 지난 후에 기름이 물들은 시트의 면적을 구하는 프로그램을 작성하시오.

입력

첫째 줄에 침대 시트의 수 N (1 ≤ N ≤ 100,000)이 주어진다.

다음 N개 줄에는 침대 시트를 나타내는 좌표 x1, y1, x2, y2가 주어진다. (x1, y1), (x2, y2)는 침대 시트의 양 끝 대각선 좌표이다. 이 좌표는 좌표평면 위의 점이 아닌 각 단위 정사각형을 나타낸다. (0, 0)을 포함하는 침대 시트는 없다.

다음 줄에는 시간의 개수 M (1 ≤ M ≤ 100,000)이 주어진다.

다음 M개 줄에는 시간이 주어진다. 이 정수는 0과 1,000,000 사이의 정수이다. 오름차순으로 주어진다.

출력

각각의 시간에 대해서, 기름에 물들은 침대 시트 영역의 크기를 출력한다.

예제 입력 1

3
-2 1 1 2
1 0 2 1
-3 -3 -2 0
2
1 2

예제 출력 1

5
15
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(x1, y1), (x2, y2)\ub294 \uce68\ub300 \uc2dc\ud2b8\uc758 \uc591 \ub05d \ub300\uac01\uc120 \uc88c\ud45c\uc774\ub2e4. \uc774 \uc88c\ud45c\ub294 \uc88c\ud45c\ud3c9\uba74 \uc704\uc758 \uc810\uc774 \uc544\ub2cc \uac01 \ub2e8\uc704 \uc815\uc0ac\uac01\ud615\uc744 \ub098\ud0c0\ub0b8\ub2e4. (0, 0)\uc744 \ud3ec\ud568\ud558\ub294 \uce68\ub300 \uc2dc\ud2b8\ub294 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0\ub294 \uc2dc\uac04\uc758 \uac1c\uc218 M (1 &le; M &le; 100,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c M\uac1c \uc904\uc5d0\ub294 \uc2dc\uac04\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc815\uc218\ub294 0\uacfc 1,000,000 \uc0ac\uc774\uc758 \uc815\uc218\uc774\ub2e4. \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \uc2dc\uac04\uc5d0 \ub300\ud574\uc11c, \uae30\ub984\uc5d0 \ubb3c\ub4e4\uc740 \uce68\ub300 \uc2dc\ud2b8 \uc601\uc5ed\uc758 \ud06c\uae30\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2928","problem_lang":"1","title":"PLAHTE","description":"<p>Mirko washed his sheets and is on his way to hang them to dry in front of his house. However, strong winds have pulled the clothesline out of the ground so Mirko temporarily laid out the sheets on the grass.&nbsp;<\/p>\r\n\r\n<p>The grass field can be modeled by an infinite square grid, where every unit square is represented by a pair of coordinates. Sheets are rectangles in the grid with sides parallel to the coordinate axes. Sheets may overlap.&nbsp;<\/p>\r\n\r\n<p>In an effort to put his clothesline back up, Mirko slammed a pole into the ground at coordinates (0, 0). An entirely unexpected turn of events followed. Oil sprung from the ground and the shock caused Mirko to faint. While Mirko lay unconscious, the oil is spreading, staining his sheets.&nbsp;<\/p>\r\n\r\n<p>Time is measured from the moment the oil starts spreading &ndash; at time zero only square (0, 0) is covered in oil. The oil is spreading at a speed of one square per second in all eight directions, as shown in the figure below. When oil enters a square, it stains that square of fabric on all sheets covering the square.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/oil(1).png\" style=\"height:180px; width:617px\" \/><\/p>\r\n\r\n<p>The grass field from the first example after zero, one and two seconds.&nbsp;<\/p>\r\n\r\n<p>Write a program that, given M points in time, calculates the total area of stained fabric on all sheets for each of the given time points.&nbsp;<\/p>\r\n","input":"<p>The first line contains an integer N (1 &le; N &le; 100 000), the number of sheets.&nbsp;<\/p>\r\n\r\n<p>Each of the following N lines contains four integers x1, y1, x2 and y2 (&minus;1 000 000 &le; x1 &le; x2 &le; 1 000 000), (&minus;1 000 000 &le; y1 &le; y2 &le; 1 000 000). The coordinates (x1, y1) and (x2, y2) represent diagonally opposite corners of a sheet (again, these coordinates are unit squares, not points on the plane). None of the sheets will cover the square (0, 0).&nbsp;<\/p>\r\n\r\n<p>The next line contains an integer M (1 &le; M &le; 100 000), the number of points in time.&nbsp;<\/p>\r\n\r\n<p>The next line contains M integers between 0 and 1 000 000, the time points. They will be given in strictly ascending order.&nbsp;<\/p>\r\n","output":"<p>For each of the time points, output on a separate line the total area of stained fabric on all sheets, in the order the time points are given in the input.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]