시간 제한메모리 제한제출정답맞힌 사람정답 비율
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문제

김주성은 사실 뛰어난 발레 실력을 숨기고 있다. 그는 매일 밤 열심히 발레 연습을 한다.

그는 항상 연습하는 곳의 바닥을 m행 n열의 정사각형 칸들로 나누어 놓고 춤을 춘다. 그가 춤을 추는 방식은 이 직사각형 격자판 위를 점프하여 돌아다니는 것인데, 현재 위치하고 있는 칸에서 점프할 수 있는 위치는 체스판 위의 나이트 (knight)가 이동할 수 있는 곳과 같다. (나이트의 이동 규칙을 모르는 경우 검색해 볼 것. ㅜ.ㅜ) 김주성은 특정한 위치에서 춤을 시작하여, 특정한 위치에서 춤을 마치고 싶다.

밤중에 쿵쿵거리면 실례이므로, 바닥에 방석을 깔아 놓고 춤을 추려고 한다. 방석은 격자칸 한 칸에 꼭 맞는 크기이고, 몇 개의 칸에는 방석이 이미 놓여 있다. 특히, 김 조교가 현재 서 있는 위치와, 최종적으로 도달하려고 하는 위치에는 이미 방석이 놓여 있다.

여러분이 할 일은 최소한의 방석을 더 놓아서 김주성의 춤이 가능하도록 만들고, 그렇게 할 수 있는 방법이 모두 몇 가지인지 계산하는 것이다. 다만, 돌멩이가 놓여 있는 칸도 있는데, 그 부분에는 방석을 놓지 않는다. 부상의 위험이 있기 때문이다.

입력

첫째 줄에 m과 n이 주어진다. (1 ≤ m, n ≤ 30)

이어지는 m개의 줄에는 각 행의 정보를 제공하는 n개의 숫자가 주어진다. 0은 맨땅, 1은 방석이 깔린 곳 중 김주성이 춤을 시작하거나 마치지 않는 위치, 2는 돌멩이가 있는 위치, 3은 김주성이 춤을 시작하는 위치 (방석이 깔려 있음), 4는 김주성이 춤을 마치는 위치 (방석이 깔려 있음)이다.

출력

첫 줄에 필요한 최소의 방석 수를 출력한다. 만약 아무리 방석을 많이 놓아도 김주성의 춤이 불가능할 경우엔, -1을 출력한다. 둘째 줄엔 방석을 놓는 방법의 수를 출력한다. (이 수는 64-bit signed integer 범위 내에 있음을 보장한다.) 만약 첫 줄에 -1을 출력한 경우에는, 둘째 줄은 출력하지 않는다.

예제 입력 1

4 5
1 0 0 0 0
3 0 0 0 0
0 0 2 0 0
0 0 0 4 0

예제 출력 1

2
3

힌트

4 5
1 0 0 0 0
3 0 0 0 0
0 0 2 0 0
0 0 0 4 0

입출력 예시의 세 가지 경우는 다음과 같다. X표 친 곳에 방석을 놓으면 된다.

1 0 0 0 0     1 0 X 0 0     1 0 X 0 0
3 0 X 0 0     3 0 0 0 0     3 0 0 0 X
0 0 2 0 0     0 X 2 0 0     0 0 2 0 0
0 X 0 4 0     0 0 0 4 0     0 0 0 4 0
[{"problem_id":"1857","problem_lang":"0","title":"\ubc1c\ub808\ub9ac\ub178","description":"<p>\uae40\uc8fc\uc131\uc740 \uc0ac\uc2e4 \ub6f0\uc5b4\ub09c \ubc1c\ub808 \uc2e4\ub825\uc744 \uc228\uae30\uace0 \uc788\ub2e4. \uadf8\ub294 \ub9e4\uc77c \ubc24 \uc5f4\uc2ec\ud788 \ubc1c\ub808 \uc5f0\uc2b5\uc744 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub294 \ud56d\uc0c1 \uc5f0\uc2b5\ud558\ub294 \uacf3\uc758 \ubc14\ub2e5\uc744 m\ud589 n\uc5f4\uc758 \uc815\uc0ac\uac01\ud615 \uce78\ub4e4\ub85c \ub098\ub204\uc5b4 \ub193\uace0 \ucda4\uc744 \ucd98\ub2e4. \uadf8\uac00 \ucda4\uc744 \ucd94\ub294 \ubc29\uc2dd\uc740 \uc774 \uc9c1\uc0ac\uac01\ud615 \uaca9\uc790\ud310 \uc704\ub97c \uc810\ud504\ud558\uc5ec \ub3cc\uc544\ub2e4\ub2c8\ub294 \uac83\uc778\ub370, \ud604\uc7ac \uc704\uce58\ud558\uace0 \uc788\ub294 \uce78\uc5d0\uc11c \uc810\ud504\ud560 \uc218 \uc788\ub294 \uc704\uce58\ub294 \uccb4\uc2a4\ud310 \uc704\uc758 \ub098\uc774\ud2b8 (knight)\uac00 \uc774\ub3d9\ud560 \uc218 \uc788\ub294 \uacf3\uacfc \uac19\ub2e4. (\ub098\uc774\ud2b8\uc758 \uc774\ub3d9 \uaddc\uce59\uc744 \ubaa8\ub974\ub294 \uacbd\uc6b0 \uac80\uc0c9\ud574 \ubcfc \uac83. \u315c.\u315c) \uae40\uc8fc\uc131\uc740 \ud2b9\uc815\ud55c \uc704\uce58\uc5d0\uc11c \ucda4\uc744 \uc2dc\uc791\ud558\uc5ec, \ud2b9\uc815\ud55c \uc704\uce58\uc5d0\uc11c \ucda4\uc744 \ub9c8\uce58\uace0 \uc2f6\ub2e4.<\/p>\r\n\r\n<p>\ubc24\uc911\uc5d0 \ucff5\ucff5\uac70\ub9ac\uba74 \uc2e4\ub840\uc774\ubbc0\ub85c, \ubc14\ub2e5\uc5d0 \ubc29\uc11d\uc744 \uae54\uc544 \ub193\uace0 \ucda4\uc744 \ucd94\ub824\uace0 \ud55c\ub2e4. \ubc29\uc11d\uc740 \uaca9\uc790\uce78 \ud55c \uce78\uc5d0 \uaf2d \ub9de\ub294 \ud06c\uae30\uc774\uace0, \uba87 \uac1c\uc758 \uce78\uc5d0\ub294 \ubc29\uc11d\uc774 \uc774\ubbf8 \ub193\uc5ec \uc788\ub2e4. \ud2b9\ud788, \uae40 \uc870\uad50\uac00 \ud604\uc7ac \uc11c \uc788\ub294 \uc704\uce58\uc640, \ucd5c\uc885\uc801\uc73c\ub85c \ub3c4\ub2ec\ud558\ub824\uace0 \ud558\ub294 \uc704\uce58\uc5d0\ub294 \uc774\ubbf8 \ubc29\uc11d\uc774 \ub193\uc5ec \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc5ec\ub7ec\ubd84\uc774 \ud560 \uc77c\uc740 \ucd5c\uc18c\ud55c\uc758 \ubc29\uc11d\uc744 \ub354 \ub193\uc544\uc11c \uae40\uc8fc\uc131\uc758 \ucda4\uc774 \uac00\ub2a5\ud558\ub3c4\ub85d \ub9cc\ub4e4\uace0, \uadf8\ub807\uac8c \ud560 \uc218 \uc788\ub294 \ubc29\ubc95\uc774 \ubaa8\ub450 \uba87 \uac00\uc9c0\uc778\uc9c0 \uacc4\uc0b0\ud558\ub294 \uac83\uc774\ub2e4. \ub2e4\ub9cc, \ub3cc\uba69\uc774\uac00 \ub193\uc5ec \uc788\ub294 \uce78\ub3c4 \uc788\ub294\ub370, \uadf8 \ubd80\ubd84\uc5d0\ub294 \ubc29\uc11d\uc744 \ub193\uc9c0 \uc54a\ub294\ub2e4. \ubd80\uc0c1\uc758 \uc704\ud5d8\uc774 \uc788\uae30 \ub54c\ubb38\uc774\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 m\uacfc n\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; m, n &le; 30)<\/p>\r\n\r\n<p>\uc774\uc5b4\uc9c0\ub294 m\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \ud589\uc758 \uc815\ubcf4\ub97c \uc81c\uacf5\ud558\ub294 n\uac1c\uc758 \uc22b\uc790\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. 0\uc740 \ub9e8\ub545, 1\uc740 \ubc29\uc11d\uc774 \uae54\ub9b0 \uacf3 \uc911 \uae40\uc8fc\uc131\uc774 \ucda4\uc744 \uc2dc\uc791\ud558\uac70\ub098 \ub9c8\uce58\uc9c0 \uc54a\ub294 \uc704\uce58, 2\ub294 \ub3cc\uba69\uc774\uac00 \uc788\ub294 \uc704\uce58, 3\uc740 \uae40\uc8fc\uc131\uc774 \ucda4\uc744 \uc2dc\uc791\ud558\ub294 \uc704\uce58 (\ubc29\uc11d\uc774 \uae54\ub824 \uc788\uc74c), 4\ub294 \uae40\uc8fc\uc131\uc774 \ucda4\uc744 \ub9c8\uce58\ub294 \uc704\uce58 (\ubc29\uc11d\uc774 \uae54\ub824 \uc788\uc74c)\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab \uc904\uc5d0 \ud544\uc694\ud55c \ucd5c\uc18c\uc758 \ubc29\uc11d \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d \uc544\ubb34\ub9ac \ubc29\uc11d\uc744 \ub9ce\uc774 \ub193\uc544\ub3c4 \uae40\uc8fc\uc131\uc758 \ucda4\uc774 \ubd88\uac00\ub2a5\ud560 \uacbd\uc6b0\uc5d4, -1\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub458\uc9f8 \uc904\uc5d4 \ubc29\uc11d\uc744 \ub193\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. (\uc774 \uc218\ub294 64-bit signed integer \ubc94\uc704 \ub0b4\uc5d0 \uc788\uc74c\uc744 \ubcf4\uc7a5\ud55c\ub2e4.) \ub9cc\uc57d \uccab \uc904\uc5d0 -1\uc744 \ucd9c\ub825\ud55c \uacbd\uc6b0\uc5d0\ub294, \ub458\uc9f8 \uc904\uc740 \ucd9c\ub825\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","hint":"<pre>\r\n4 5\r\n1 0 0 0 0\r\n3 0 0 0 0\r\n0 0 2 0 0\r\n0 0 0 4 0<\/pre>\r\n\r\n<p>\uc785\ucd9c\ub825 \uc608\uc2dc\uc758 \uc138 \uac00\uc9c0 \uacbd\uc6b0\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4. X\ud45c \uce5c \uacf3\uc5d0 \ubc29\uc11d\uc744 \ub193\uc73c\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<pre>\r\n1 0 0 0 0     1 0 X 0 0     1 0 X 0 0\r\n3 0 X 0 0     3 0 0 0 0     3 0 0 0 X\r\n0 0 2 0 0     0 X 2 0 0     0 0 2 0 0\r\n0 X 0 4 0     0 0 0 4 0     0 0 0 4 0<\/pre>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"1857","problem_lang":"1","title":"Lilypad Pond","description":"<p>FJ has installed a beautiful pond for his cows&#39; aesthetic enjoyment and exercise.<\/p>\r\n\r\n<p>The rectangular pond has been partitioned into square cells of M rows and N columns (1 &lt;= M &lt;= 30; 1 &lt;= N &lt;= 30). Some of the cells have astonishingly sturdy lilypads; others have rocks; the remainder are just beautiful, cool, blue water.<\/p>\r\n\r\n<p>Bessie is practicing her ballet moves by jumping from one lilypad to another and is currently located at one of the lilypads. She wants to travel to another lilypad in the pond by jumping from one lilypad to another.<\/p>\r\n\r\n<p>Surprising only to the uninitiated, Bessie&#39;s jumps between lilypads always appear as a chess-knight&#39;s move: one move in one direction and then two more in the orthogonal direction (or perhaps two in one direction and then one in the orthogonal direction).<\/p>\r\n\r\n<p>Farmer John is observing Bessie&#39;s ballet drill and realizes that sometimes she might not be able to jump to her destination lilypad because intermediary lilypads are missing.<\/p>\r\n\r\n<p>Ever thrifty, he wants to place additional lilypads so she can complete her quest (perhaps quickly, perhaps by using a large number of intermediate lilypads). Of course, lilypads cannot be placed where rocks already intrude on a cell.<\/p>\r\n\r\n<p>Help Farmer John determine the minimum number of additional lilypads he has to place, and in how many ways he can place that minimum number.<\/p>\r\n","input":"<p>* Line 1: Two space-separated integers: M and N<\/p>\r\n\r\n<p>* Lines 2..M+1: Line i+1 describes row i of the pond using N space-separated integers with these values: 0 indicates empty water; 1 indicates a lilypad in place; 2 indicates rock in place; 3 indicates the lilypad Bessie starts on; 4 indicates the lilypad Bessie wants to travel to.<\/p>\r\n","output":"<p>* Line 1: One integer: the minimum number of additional lilypads required. If it is not possible to help Bessie jump to her destination, print -1.<\/p>\r\n\r\n<p>* Line 2: One integer: the total number of possible ways the additional lilypads can be positioned. &nbsp;This number is guaranteed to fit into a single 64-bit signed integer. Do not output this line if line 1 contains -1.<\/p>\r\n","hint":"<p>The ponds has 4 rows and 5 columns. Bessie is at row 2 column 1, and she wants to reach row 4 column 4. A rock and three lilypads are present.<\/p>\r\n\r\n<p>Two lilypads are required. There are three ways to place them: row 4 column 2 and row 2 column 3; row 1 column 3 and row 3 column 2; or row 1 column 3 and row 2 column 5:<\/p>\r\n\r\n<pre>\r\n          R1C2,R2C3     R1C3,R3C2     R1C3,R2C5\r\n          1 0 0 0 0     1 0 X 0 0     1 0 X 0 0\r\n          3 0 X 0 0     3 0 0 0 0     3 0 0 0 X\r\n          0 0 2 0 0     0 X 2 0 0     0 0 2 0 0\r\n          0 X 0 4 0     0 0 0 4 0     0 0 0 4 0\r\n<\/pre>","original":"1","html_title":"0","problem_lang_tcode":"English"}]