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문제

대학교를 졸업한 준규는 농부의 꿈을 이루기 위해서 가로 5m, 세로 5m 크기의 땅을 구입했다. 준규는 땅을 가로 1m, 세로 1m 크기로 구역을 나누었다. 가장 왼쪽 위 칸은 (1,1)이고 가장 오른쪽 아래 칸은 (5,5)이다. 준규의 땅을 아래 그림과 같이 나타낼 수 있다.

(1,1) (1,2) (1,3) (1,4) (1,5)
(2,1) (2,2) (2,3) (2,4) (2,5)
(3,1) (3,2) (3,3) (3,4) (3,5)
(4,1) (4,2) (4,3) (4,4) (4,5)
(5,1) (5,2) (5,3) (5,4) (5,5)

구역 K개를 제외한 각각의 구역에는 사과 나무가 하나씩 심어져 있다. K개 구역에는 거대한 돌이 있기 때문에 사과 나무가 심어져 있지 않다.

사과를 수확하는 일은 매우 귀찮은 일이다. 따라서, 준규는 친구 해빈이와 함께 재밌는 방법으로 수확을 하려고 한다.

준규는 (1,1)에서 사과를 수확하기 시작하고, 해빈이는 (5,5)에서 시작한다. (1,1)과 (5,5)에는 항상 사과 나무가 심어져 있다.

사과 나무 하나에 있는 모든 사과를 수확하는데 걸리는 시간은 항상 30분이다. 준규와 해빈이가 현재 있는 칸의 사과 나무에서 사과를 모두 수확하면, 인접한 칸 중 사과 나무가 있는 칸으로 이동한다. 이동하는데 걸리는 시간도 30분이다.

준규와 해빈이는 준규의 땅에 있는 모든 사과를 수확할 것이고, 마지막에는 같은 칸에서 만나려고 한다. 이 때, 이렇게 사과를 수확하는 방법의 수를 구하는 프로그램을 작성하시오.

두 사람은 항상 사과가 있는 칸으로만 이동하며, 이미 수확을 마친 사과 나무가 있는 칸으로는 이동하지 않는다. 또, 마지막을 제외하고 같은 칸에서 만날 수는 없다.

입력

첫째 줄에 K가 주어진다. 둘째 줄부터 K (0 ≤ K ≤ 22, K는 짝수)개 줄에는 사과 나무가 없는 칸의 위치 (i,j)가 주어진다.

출력

문제에서 주어진 방법대로 사과를 모두 수확하는 방법의 수를 출력한다.

예제 입력 1

4
3 2
3 3
3 4
3 1

예제 출력 1

1

힌트

입력으로 주어진 상황을 그림으로 그리면 아래와 같다. 점(.)은 사과 나무가 있는 칸, x는 없는 칸을 나타내며, j는 준규의 위치, h는 해빈이의 위치이다.

j  .  .  .  .

.  .  .  .  .

x  x  x  x  .

.  .  .  .  .

.  .  .  .  h

문제의 조건을 지키면서 사과를 모두 수확하는 방법은 한가지이며, 아래와 같다.

j  j--j  j--j
|  |  |  |  |
j--j  j--j  j
            |
x  x  x  x j/h
            |
h--h--h--h--h
|
h--h--h--h--h
[{"problem_id":"5913","problem_lang":"0","title":"\uc900\uaddc\uc640 \uc0ac\uacfc","description":"<p>\ub300\ud559\uad50\ub97c \uc878\uc5c5\ud55c \uc900\uaddc\ub294 \ub18d\ubd80\uc758 \uafc8\uc744 \uc774\ub8e8\uae30 \uc704\ud574\uc11c \uac00\ub85c 5m, \uc138\ub85c 5m \ud06c\uae30\uc758 \ub545\uc744 \uad6c\uc785\ud588\ub2e4. \uc900\uaddc\ub294 \ub545\uc744 \uac00\ub85c 1m, \uc138\ub85c 1m \ud06c\uae30\ub85c \uad6c\uc5ed\uc744 \ub098\ub204\uc5c8\ub2e4. \uac00\uc7a5 \uc67c\ucabd \uc704 \uce78\uc740 (1,1)\uc774\uace0 \uac00\uc7a5 \uc624\ub978\ucabd \uc544\ub798 \uce78\uc740 (5,5)\uc774\ub2e4. \uc900\uaddc\uc758 \ub545\uc744 \uc544\ub798 \uadf8\ub9bc\uacfc \uac19\uc774 \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<pre>\r\n(1,1) (1,2) (1,3) (1,4) (1,5)\r\n(2,1) (2,2) (2,3) (2,4) (2,5)\r\n(3,1) (3,2) (3,3) (3,4) (3,5)\r\n(4,1) (4,2) (4,3) (4,4) (4,5)\r\n(5,1) (5,2) (5,3) (5,4) (5,5)<\/pre>\r\n\r\n<p>\uad6c\uc5ed K\uac1c\ub97c \uc81c\uc678\ud55c \uac01\uac01\uc758 \uad6c\uc5ed\uc5d0\ub294 \uc0ac\uacfc \ub098\ubb34\uac00 \ud558\ub098\uc529 \uc2ec\uc5b4\uc838 \uc788\ub2e4. K\uac1c \uad6c\uc5ed\uc5d0\ub294 \uac70\ub300\ud55c \ub3cc\uc774 \uc788\uae30 \ub54c\ubb38\uc5d0 \uc0ac\uacfc \ub098\ubb34\uac00 \uc2ec\uc5b4\uc838 \uc788\uc9c0 \uc54a\ub2e4.<\/p>\r\n\r\n<p>\uc0ac\uacfc\ub97c \uc218\ud655\ud558\ub294 \uc77c\uc740 \ub9e4\uc6b0 \uadc0\ucc2e\uc740 \uc77c\uc774\ub2e4. \ub530\ub77c\uc11c, \uc900\uaddc\ub294 \uce5c\uad6c \ud574\ube48\uc774\uc640 \ud568\uaed8 \uc7ac\ubc0c\ub294 \ubc29\ubc95\uc73c\ub85c \uc218\ud655\uc744 \ud558\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc900\uaddc\ub294 (1,1)\uc5d0\uc11c \uc0ac\uacfc\ub97c \uc218\ud655\ud558\uae30 \uc2dc\uc791\ud558\uace0, \ud574\ube48\uc774\ub294 (5,5)\uc5d0\uc11c \uc2dc\uc791\ud55c\ub2e4. (1,1)\uacfc (5,5)\uc5d0\ub294 \ud56d\uc0c1 \uc0ac\uacfc \ub098\ubb34\uac00 \uc2ec\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc0ac\uacfc \ub098\ubb34 \ud558\ub098\uc5d0 \uc788\ub294 \ubaa8\ub4e0 \uc0ac\uacfc\ub97c \uc218\ud655\ud558\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\uc740 \ud56d\uc0c1 30\ubd84\uc774\ub2e4. \uc900\uaddc\uc640 \ud574\ube48\uc774\uac00 \ud604\uc7ac \uc788\ub294 \uce78\uc758 \uc0ac\uacfc \ub098\ubb34\uc5d0\uc11c \uc0ac\uacfc\ub97c \ubaa8\ub450 \uc218\ud655\ud558\uba74, \uc778\uc811\ud55c \uce78 \uc911 \uc0ac\uacfc \ub098\ubb34\uac00 \uc788\ub294 \uce78\uc73c\ub85c \uc774\ub3d9\ud55c\ub2e4. \uc774\ub3d9\ud558\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\ub3c4 30\ubd84\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc900\uaddc\uc640 \ud574\ube48\uc774\ub294 \uc900\uaddc\uc758 \ub545\uc5d0 \uc788\ub294 \ubaa8\ub4e0 \uc0ac\uacfc\ub97c \uc218\ud655\ud560 \uac83\uc774\uace0, \ub9c8\uc9c0\ub9c9\uc5d0\ub294 \uac19\uc740 \uce78\uc5d0\uc11c \ub9cc\ub098\ub824\uace0 \ud55c\ub2e4. \uc774 \ub54c, \uc774\ub807\uac8c \uc0ac\uacfc\ub97c \uc218\ud655\ud558\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\ub450 \uc0ac\ub78c\uc740 \ud56d\uc0c1 \uc0ac\uacfc\uac00 \uc788\ub294 \uce78\uc73c\ub85c\ub9cc \uc774\ub3d9\ud558\uba70, \uc774\ubbf8 \uc218\ud655\uc744 \ub9c8\uce5c \uc0ac\uacfc \ub098\ubb34\uac00 \uc788\ub294 \uce78\uc73c\ub85c\ub294 \uc774\ub3d9\ud558\uc9c0 \uc54a\ub294\ub2e4. \ub610, \ub9c8\uc9c0\ub9c9\uc744 \uc81c\uc678\ud558\uace0 \uac19\uc740 \uce78\uc5d0\uc11c \ub9cc\ub0a0 \uc218\ub294 \uc5c6\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 K\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\ubd80\ud130 K (0 &le; K &le;&nbsp;22, K\ub294 \uc9dd\uc218)\uac1c \uc904\uc5d0\ub294 \uc0ac\uacfc \ub098\ubb34\uac00 \uc5c6\ub294 \uce78\uc758 \uc704\uce58 (i,j)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\ubb38\uc81c\uc5d0\uc11c \uc8fc\uc5b4\uc9c4 \ubc29\ubc95\ub300\ub85c \uc0ac\uacfc\ub97c \ubaa8\ub450 \uc218\ud655\ud558\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uc0c1\ud669\uc744 \uadf8\ub9bc\uc73c\ub85c \uadf8\ub9ac\uba74 \uc544\ub798\uc640 \uac19\ub2e4. \uc810(.)\uc740 \uc0ac\uacfc \ub098\ubb34\uac00 \uc788\ub294 \uce78, x\ub294 \uc5c6\ub294 \uce78\uc744 \ub098\ud0c0\ub0b4\uba70, j\ub294 \uc900\uaddc\uc758 \uc704\uce58, h\ub294 \ud574\ube48\uc774\uc758 \uc704\uce58\uc774\ub2e4.<\/p>\r\n\r\n<pre>\r\nj  .  .  .  .\r\n\r\n.  .  .  .  .\r\n\r\nx  x  x  x  .\r\n\r\n.  .  .  .  .\r\n\r\n.  .  .  .  h\r\n<\/pre>\r\n\r\n<p>\ubb38\uc81c\uc758 \uc870\uac74\uc744 \uc9c0\ud0a4\uba74\uc11c \uc0ac\uacfc\ub97c \ubaa8\ub450 \uc218\ud655\ud558\ub294 \ubc29\ubc95\uc740 \ud55c\uac00\uc9c0\uc774\uba70, \uc544\ub798\uc640 \uac19\ub2e4.<\/p>\r\n\r\n<pre>\r\nj  j--j  j--j\r\n|  |  |  |  |\r\nj--j  j--j  j\r\n            |\r\nx  x  x  x j\/h\r\n            |\r\nh--h--h--h--h\r\n|\r\nh--h--h--h--h\r\n<\/pre>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5913","problem_lang":"1","title":"Grazing Patterns","description":"<p>Due to recent budget cuts, FJ has downsized his farm so that the grazing area for his cows is only a 5 meter by 5 meter square field! &nbsp;The field is laid out like a 5x5 grid of 1 meter by 1 meter squares, with (1,1) being the location of the upper-left square, and (5,5) being the location of the lower-right square:<\/p>\r\n\r\n<pre>\r\n(1,1) (1,2) (1,3) (1,4) (1,5)\r\n(2,1) (2,2) (2,3) (2,4) (2,5)\r\n(3,1) (3,2) (3,3) (3,4) (3,5)\r\n(4,1) (4,2) (4,3) (4,4) (4,5)\r\n(5,1) (5,2) (5,3) (5,4) (5,5)<\/pre>\r\n\r\n<p>Every square in this grid is filled with delicious grass, except for K barren squares (0 &lt;= K &lt;= 22, K even), which have no grass. &nbsp;Bessie the cow starts grazing in square (1,1), which is always filled with grass, and Mildred the cow starts grazing in square (5,5), which also is always filled with grass. &nbsp;<\/p>\r\n\r\n<p>Each half-hour, Bessie and Mildred finish eating all the grass in their respective squares and each both move to adjacent grassy squares (north, south, east, or west). &nbsp;They want to consume all the grassy squares and end up in exactly the same final location. &nbsp;Please compute the number of different ways this can happen. &nbsp;Bessie and Mildred always move onto grassy squares, and they never both move onto the same square unless that is the very last grassy square remaining.<\/p>\r\n","input":"<p>* Line 1: The integer K.<\/p>\r\n\r\n<p>* Lines 2..1+K: Each line contains the location (i,j) of a non-grassy square by listing the two space-separated integers i and j.<\/p>\r\n","output":"<p>* Line 1: The number of different possible ways Bessie and Mildred can walk across the field to eat all the grass and end up in the same final location.<\/p>\r\n","hint":"<p>The initial grid looks like this (where . denotes a grassy square, x denotes a non-grassy square, b indicates the starting location of Bessie, and m indicates the starting location of Mildred):<\/p>\r\n\r\n<pre>\r\nj  .  .  .  .\r\n\r\n.  .  .  .  .\r\n\r\nx  x  x  x  .\r\n\r\n.  .  .  .  .\r\n\r\n.  .  .  .  h\r\n<\/pre>\r\n\r\n<p>There is only one possible solution, with Bessie and Mildred meeting at square (3,5):<\/p>\r\n\r\n<pre>\r\nj  j--j  j--j\r\n|  |  |  |  |\r\nj--j  j--j  j\r\n            |\r\nx  x  x  x j\/h\r\n            |\r\nh--h--h--h--h\r\n|\r\nh--h--h--h--h<font face=\"sans-serif, Arial, Verdana, Trebuchet MS\"><span style=\"white-space:normal\">\r\n<\/span><\/font><\/pre>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > USA Computing Olympiad > 2011-2012 Season > USACO January 2012 Contest > Bronze 3번